Ram Raj Science Institute
ROTATIONAL DYNAMICS
Theory
1) What is the value of tangential acceleration in U.C.M. 1
2) Obtain the relation between linear velocity and angular velocity in U.C.M. (March 2008, 2012, Oct. 2009) 2
3) Define radius of gyration. Explain its physical significance. ( March 2008, 2019, July 2018) 2
4) Derive an expression for the kinetic energy of body rotating with uniform angular speed.(March 2009) 2
5) Distinguish between centripetal force and centrifugal force. ( March 2009, 2010, 2018 ) 2
6) State and prove the law of conservation of angular momentum. ( March 2011, 2018, Oct. 2011, 2015) 2
7) Define centripetal force and give its any two examples. ( March 2011) 2
8) State S.I. unit of angular momentum. Obtain its dimensions. (March 2012) 2
9) For a particle performing uniform circular motion ν = ω × r . Obtain an expression of linear acceleration of 2
the particle performing non-uniform circular motion. ( Feb- 2014)
10) State the law of conservation of angular momentum and explain with a suitable example. ( Oct.2014) 2
11) In circular motion assuming ν = ω × r , Obtain an expression for the resultant acceleration of a particle in 2
terms of tangential and radial component. ( Feb 2015)
12) State the theorem of parallel axes and theorem of perpendicular axes about moment of inertia ( Feb 2015) 2
13) Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length 2
( Oct. 2015)
14) In U.C.M. ( Uniform Circular Motion), Prove the relation ν = ω × r , where symbols have their usual 2
meanings. ( Feb 2016)
2 K2
15) 1 2
Obtain an expression for total kinetic energy of a rolling body in the form MV 1 + 2 ( Feb 2016)
2 R
16) Draw a neat labelled diagram showing the various forces and their components acting on a vehicle moving along 2
curved banked road. ( July 2016)
17) Explain the concept of centripetal force. ( March 2017) ` 2
18) Explain the physical significance of radius gyration. ( July 2017) 2
1) Derive an expression for linear acceleration of a particle performing U.C.M. 3
2) Derive an expression for period of a conical pendulum. ( March 2008) 3
3) 1 3
Show that the kinetic energy of a rotating body about a given axis is equal to Lω . Where L is angular
2
momentum and ω is angular velocity. (March 2008)
4) Define momentum of inertia. State its SI unit and dimensions. ( Oct 2008, March 2018) 3
5) v 2 3
For a conical pendulum prove that tan θ = ( Oct. 2009)
rg
6) Obtain an expression for maximum speed with which a vehicle can be driven safely on a banked road. Show 3
that the safety speed limit is independent of the mass of the vehicle. ( march 2010, Oct 2010)
7) State and prove the principle of perpendicular axis. ( March 2010) 3
8) Show that total energy of a body performing vertical circular motion is conserved. ( March 2011) 3
9) Derive an expression for linear velocity at lowest point and at highest point for a particle revolving in vertical 3
circular motion. ( Oct 2011)
10) What is banking of roads ? Obtain an expression for the maximum safety speed of a vehicle moving along a
curve horizontal road. ( March 2012)
11) Derive an expression for a kinetic energy of a body of mass M rotating uniformly about a given axis. Show that 3
2
1 L
the rotational kinetic energy = × ( March 2012)
2M K
,12) Derive an expression for kinetic energy, when rigid body is rolling on a horizontal surface without slipping. 3
Hence find kinetic energy for a solid sphere. ( March 2013)
13) A particle of mass m, just completes the vertical circular motion. Derive the expression for the difference in 3
tensions at the highest and the lowest points. ( March 2013)
14) Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road. Write 3
the necessary equation for maximum safety and state the significance of each involved in it. ( Oct 2014)
15) Obtain an expression for torque acting on a body rotating with uniform angular acceleration. 3
( July 2016 , 2017)
16) Obtain an expression of energy of a particle at different positions in the vertical circular motion.( March 2019) 3
1) State and prove the theorem of Parallel axis. ( Feb 2014, 2016) 4
2) State an expression for the moment of inertia of a solid uniform disc, rotating about an axis passing through its 4
centre. Perpendicular to its plane. Hence derive and expression for the moment of inertia and radius of gyration
i) about a tangent in the plane of the disc, and ii) about a tangent perpendicular to the plane of the disc.
( Oct 2015)
Problems :
1) An object of mass 1kg is tied to one end of a string of length 9 m and whirled in a vertical circle. What is the 2
minimum speed required at the lowest position to complete a circle ? ( Oct 2008)
2
2) A torque of magnitude of 1500 Nm acting on a body produces an angular acceleration of 3.2 rad /s . Find M.I. 2
of the body. ( March 2009)
3) A torque of magnitude of 1000 Nm acting on a body produces an angular acceleration of 2 rad / s 2. Calculate 2
the moment inertia of the body. ( Oct 2009 , March 2010 )
4) Moment of a inertia of a disc about an axis passing through its centre and perpendicular to its plane is 10 kg-m2 2
Find its moment of inertia about the diameter. ( Oct 2010)
5) A stone of mass one kilogram is tied to the end of a string of length 5m and whirled in a vertical. What will be 2
the minimum speed required at lowest position to complete the circle. (Oct 2010)
6) A coin kept on a horizontal rotating disc has its centre at a distance of 0.1 m form the axis of the rotating disc. 2
If the coefficient of fraction between the coin and the disc is 0.25; find the angular speed of disc at which the
coin would be about to slip off. ( Given: g = 9.8 m/s2) ( Oct 2011)
7) A car of mass 1500kg rounds a curve of radius 250 m at 90km/hour. Calculate the centripetal force acting on it. 2
(March 2013)
8) A wheel of moment of inertia 1 kgm2 is rotating at a speed of 40 rad /s. Due to friction on the axis, the wheel 2
comes to rest in 10 minutes. Calculate the angular momentum of the wheel, two minutes before it comes to rest.
( March 2013, March 2019 )
9) A racing car completes 5 rounds on a circular track in 2 minutes. Find the radius of the track if the car has 2
uniform centripetal acceleration of π2 m / s2 ( Oct 2013)
10) A stone of mass 1 kg is whirled in horizontal circle attached at the end of a 1m long string. If the string makes 2
an angle of 300 with vertical, calculate the centripetal force acting on the stone. ( g = 9.8m / s2) (Feb 2014)
11) A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 12cm, calculate its moment 2
of inertia about an axis passing through its centre and perpendicular to its length. ( Feb 2014)
12) A stone of mass 5 kg tide to one end of rope of length 0.8m. is whirled in a vertical circle. Find the minimum 2
velocity at the highest point and at the midway point. [g = 9.8m / s2] ( Oct 2014)
13) The spin dryer of a washing machine rotating at 15 r.p.s. slow down to 5 r.p.s. after making 50 revolutions Find 2
the angular acceleration. ( Feb 2015)
14) A coin kept at a distance of 5cm from the centre of a turntable of radius 1.5m just begins to slip when the 2
turntable rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the
turntable. [g = 9.8m / s2]
15) A stone of mass 2 kg is whirled in a horizontal circle attached at the end of 1.5 m long string. If the string makes 2
an angle 300 with vertical, compute its period. [g = 9.8m / s2] ( July 2016)
, 16) A uniform solid sphere has a radius 0.1 m and density 6 × 103 kg / m3. Find its moment of inertia about a tangent 2
to its surface. ( July 2016)
17) A solid sphere of mass 1 kg rolls on a table with linear speed 2 m/s find total kinetic energy. ( March 2017) 2
18) A small body of a mass 0.3 kg oscillates in vertical plane with the help of string 0.5 m long with constant speed 2
of 2 m /s. It makes angle of 600 with the vertical. Calculate tension in the string. [g = 9.8m / s2] (July2017)
19) A flat curve on a highway has a radius of curvature 400m. A car goes around a curve at a speed 32 m/s What is 2
the minimum value of coefficient of friction that will prevent the car from sliding ? [g = 9.8m / s 2]
( March 2018)
20) The frequency of revolution of a particle performing circular motion changes from 60 r.p.m. to 180 r.p.m. in 20 2
seconds. Calculate the angular acceleration of the particle. [ π = 3.142] ( July 2018)
21) The radius of gyration of a body about an axis, at a distance of 0.4 m from the centre of mass 0.5m. Find the 2
radius of gyration about a parallel axis passing through its centre of mass. ( March 2019)
1) A ballet dancer spins about a vertical axis at 2.5 π rad /sec. with his both arms outstretched. With the arms 3
folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new rotation in
r.p.m. ( Oct 2013)
2) In a conical pendulum a string of length 120 cm is fixed at rigid support and carries a mass of 150 g at its free 3
end. If the mass is revolved in horizontal circle of radius 0.2 m around a vertical axis. Calculate tension in the
string. [g = 9.8m / s2] ( Oct. 2013)
3) A horizontal disc is freely rotating about a transverse axis passing through its centre at the rate of 100 revolutions 3
per minute. A 20 grm blob of wax falls on the disc and sticks to the disc at a distance of 5 cm from its axis
Moment of inertia of the disc about its axis passing through its centre of mass is 2 × 10 –4 kgm2. Calculate the
new frequency of rotation of the disc. ( Feb 2015)
4) A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at 3
lowest point as 7 m/s. Find the velocity at the highest point. Acceleration due to gravity = 9.8m / s2]
(Oct 2015)
5) A vehicle is moving on a circular track whose surface is inclined towards the horizontal at an angle of 100. The 3
maximum velocity with which it can safely is 36 km/hr. Calculate the length of the circular track.
[ π = 3.142] ( March 2017)
6) A uniform solid sphere has radius 0.2 m and density 8 × 103 kg m3. Find the moment of inertia about the tangent 3
of its surface. [ π = 3.142] ( July 2017)
7) A meter gauge train is moving at 72 km / hr along a curved railway of radius of curvature 500 m at a certain 3
place. Find the elevation of outer rail above the inner rail so that there is no side pressure on the rail.
[g = 9.8m / s2] ( July. 2018)
8) A solid sphere of diameter 50cm and mass 25 kg rotates about an axis through its centre. Calculate its moment 3
of inertia . If its angular velocity changes from 2 rad/s to 1 rad / sin 5 seconds, calculate the torque applied.
(July 2018)
1) An object of mass 2 kg attached to a wire length 5 m is revolved in a horizontal circle. If it makes 60 r.p.m. find 4
its. ( March 2009)
i) Angular speed ii) Linear iii) Centripetal iv) Centripetal force.
speed acceleration
MECHANICAL PROPERTIES OF FLUID
Theory
1) Define the terms : a) Sphere of influence b) Angle of contact . ( march 2008) 2
2) Define surface tension. State its S.I. unit and dimensions. ( March 2009) 2
3) Draw a neat diagram for the rise of liquid in the capillary tube showing the components of a surface tension. 2
( March 2010 , July 2016)
ROTATIONAL DYNAMICS
Theory
1) What is the value of tangential acceleration in U.C.M. 1
2) Obtain the relation between linear velocity and angular velocity in U.C.M. (March 2008, 2012, Oct. 2009) 2
3) Define radius of gyration. Explain its physical significance. ( March 2008, 2019, July 2018) 2
4) Derive an expression for the kinetic energy of body rotating with uniform angular speed.(March 2009) 2
5) Distinguish between centripetal force and centrifugal force. ( March 2009, 2010, 2018 ) 2
6) State and prove the law of conservation of angular momentum. ( March 2011, 2018, Oct. 2011, 2015) 2
7) Define centripetal force and give its any two examples. ( March 2011) 2
8) State S.I. unit of angular momentum. Obtain its dimensions. (March 2012) 2
9) For a particle performing uniform circular motion ν = ω × r . Obtain an expression of linear acceleration of 2
the particle performing non-uniform circular motion. ( Feb- 2014)
10) State the law of conservation of angular momentum and explain with a suitable example. ( Oct.2014) 2
11) In circular motion assuming ν = ω × r , Obtain an expression for the resultant acceleration of a particle in 2
terms of tangential and radial component. ( Feb 2015)
12) State the theorem of parallel axes and theorem of perpendicular axes about moment of inertia ( Feb 2015) 2
13) Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length 2
( Oct. 2015)
14) In U.C.M. ( Uniform Circular Motion), Prove the relation ν = ω × r , where symbols have their usual 2
meanings. ( Feb 2016)
2 K2
15) 1 2
Obtain an expression for total kinetic energy of a rolling body in the form MV 1 + 2 ( Feb 2016)
2 R
16) Draw a neat labelled diagram showing the various forces and their components acting on a vehicle moving along 2
curved banked road. ( July 2016)
17) Explain the concept of centripetal force. ( March 2017) ` 2
18) Explain the physical significance of radius gyration. ( July 2017) 2
1) Derive an expression for linear acceleration of a particle performing U.C.M. 3
2) Derive an expression for period of a conical pendulum. ( March 2008) 3
3) 1 3
Show that the kinetic energy of a rotating body about a given axis is equal to Lω . Where L is angular
2
momentum and ω is angular velocity. (March 2008)
4) Define momentum of inertia. State its SI unit and dimensions. ( Oct 2008, March 2018) 3
5) v 2 3
For a conical pendulum prove that tan θ = ( Oct. 2009)
rg
6) Obtain an expression for maximum speed with which a vehicle can be driven safely on a banked road. Show 3
that the safety speed limit is independent of the mass of the vehicle. ( march 2010, Oct 2010)
7) State and prove the principle of perpendicular axis. ( March 2010) 3
8) Show that total energy of a body performing vertical circular motion is conserved. ( March 2011) 3
9) Derive an expression for linear velocity at lowest point and at highest point for a particle revolving in vertical 3
circular motion. ( Oct 2011)
10) What is banking of roads ? Obtain an expression for the maximum safety speed of a vehicle moving along a
curve horizontal road. ( March 2012)
11) Derive an expression for a kinetic energy of a body of mass M rotating uniformly about a given axis. Show that 3
2
1 L
the rotational kinetic energy = × ( March 2012)
2M K
,12) Derive an expression for kinetic energy, when rigid body is rolling on a horizontal surface without slipping. 3
Hence find kinetic energy for a solid sphere. ( March 2013)
13) A particle of mass m, just completes the vertical circular motion. Derive the expression for the difference in 3
tensions at the highest and the lowest points. ( March 2013)
14) Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road. Write 3
the necessary equation for maximum safety and state the significance of each involved in it. ( Oct 2014)
15) Obtain an expression for torque acting on a body rotating with uniform angular acceleration. 3
( July 2016 , 2017)
16) Obtain an expression of energy of a particle at different positions in the vertical circular motion.( March 2019) 3
1) State and prove the theorem of Parallel axis. ( Feb 2014, 2016) 4
2) State an expression for the moment of inertia of a solid uniform disc, rotating about an axis passing through its 4
centre. Perpendicular to its plane. Hence derive and expression for the moment of inertia and radius of gyration
i) about a tangent in the plane of the disc, and ii) about a tangent perpendicular to the plane of the disc.
( Oct 2015)
Problems :
1) An object of mass 1kg is tied to one end of a string of length 9 m and whirled in a vertical circle. What is the 2
minimum speed required at the lowest position to complete a circle ? ( Oct 2008)
2
2) A torque of magnitude of 1500 Nm acting on a body produces an angular acceleration of 3.2 rad /s . Find M.I. 2
of the body. ( March 2009)
3) A torque of magnitude of 1000 Nm acting on a body produces an angular acceleration of 2 rad / s 2. Calculate 2
the moment inertia of the body. ( Oct 2009 , March 2010 )
4) Moment of a inertia of a disc about an axis passing through its centre and perpendicular to its plane is 10 kg-m2 2
Find its moment of inertia about the diameter. ( Oct 2010)
5) A stone of mass one kilogram is tied to the end of a string of length 5m and whirled in a vertical. What will be 2
the minimum speed required at lowest position to complete the circle. (Oct 2010)
6) A coin kept on a horizontal rotating disc has its centre at a distance of 0.1 m form the axis of the rotating disc. 2
If the coefficient of fraction between the coin and the disc is 0.25; find the angular speed of disc at which the
coin would be about to slip off. ( Given: g = 9.8 m/s2) ( Oct 2011)
7) A car of mass 1500kg rounds a curve of radius 250 m at 90km/hour. Calculate the centripetal force acting on it. 2
(March 2013)
8) A wheel of moment of inertia 1 kgm2 is rotating at a speed of 40 rad /s. Due to friction on the axis, the wheel 2
comes to rest in 10 minutes. Calculate the angular momentum of the wheel, two minutes before it comes to rest.
( March 2013, March 2019 )
9) A racing car completes 5 rounds on a circular track in 2 minutes. Find the radius of the track if the car has 2
uniform centripetal acceleration of π2 m / s2 ( Oct 2013)
10) A stone of mass 1 kg is whirled in horizontal circle attached at the end of a 1m long string. If the string makes 2
an angle of 300 with vertical, calculate the centripetal force acting on the stone. ( g = 9.8m / s2) (Feb 2014)
11) A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 12cm, calculate its moment 2
of inertia about an axis passing through its centre and perpendicular to its length. ( Feb 2014)
12) A stone of mass 5 kg tide to one end of rope of length 0.8m. is whirled in a vertical circle. Find the minimum 2
velocity at the highest point and at the midway point. [g = 9.8m / s2] ( Oct 2014)
13) The spin dryer of a washing machine rotating at 15 r.p.s. slow down to 5 r.p.s. after making 50 revolutions Find 2
the angular acceleration. ( Feb 2015)
14) A coin kept at a distance of 5cm from the centre of a turntable of radius 1.5m just begins to slip when the 2
turntable rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the
turntable. [g = 9.8m / s2]
15) A stone of mass 2 kg is whirled in a horizontal circle attached at the end of 1.5 m long string. If the string makes 2
an angle 300 with vertical, compute its period. [g = 9.8m / s2] ( July 2016)
, 16) A uniform solid sphere has a radius 0.1 m and density 6 × 103 kg / m3. Find its moment of inertia about a tangent 2
to its surface. ( July 2016)
17) A solid sphere of mass 1 kg rolls on a table with linear speed 2 m/s find total kinetic energy. ( March 2017) 2
18) A small body of a mass 0.3 kg oscillates in vertical plane with the help of string 0.5 m long with constant speed 2
of 2 m /s. It makes angle of 600 with the vertical. Calculate tension in the string. [g = 9.8m / s2] (July2017)
19) A flat curve on a highway has a radius of curvature 400m. A car goes around a curve at a speed 32 m/s What is 2
the minimum value of coefficient of friction that will prevent the car from sliding ? [g = 9.8m / s 2]
( March 2018)
20) The frequency of revolution of a particle performing circular motion changes from 60 r.p.m. to 180 r.p.m. in 20 2
seconds. Calculate the angular acceleration of the particle. [ π = 3.142] ( July 2018)
21) The radius of gyration of a body about an axis, at a distance of 0.4 m from the centre of mass 0.5m. Find the 2
radius of gyration about a parallel axis passing through its centre of mass. ( March 2019)
1) A ballet dancer spins about a vertical axis at 2.5 π rad /sec. with his both arms outstretched. With the arms 3
folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new rotation in
r.p.m. ( Oct 2013)
2) In a conical pendulum a string of length 120 cm is fixed at rigid support and carries a mass of 150 g at its free 3
end. If the mass is revolved in horizontal circle of radius 0.2 m around a vertical axis. Calculate tension in the
string. [g = 9.8m / s2] ( Oct. 2013)
3) A horizontal disc is freely rotating about a transverse axis passing through its centre at the rate of 100 revolutions 3
per minute. A 20 grm blob of wax falls on the disc and sticks to the disc at a distance of 5 cm from its axis
Moment of inertia of the disc about its axis passing through its centre of mass is 2 × 10 –4 kgm2. Calculate the
new frequency of rotation of the disc. ( Feb 2015)
4) A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at 3
lowest point as 7 m/s. Find the velocity at the highest point. Acceleration due to gravity = 9.8m / s2]
(Oct 2015)
5) A vehicle is moving on a circular track whose surface is inclined towards the horizontal at an angle of 100. The 3
maximum velocity with which it can safely is 36 km/hr. Calculate the length of the circular track.
[ π = 3.142] ( March 2017)
6) A uniform solid sphere has radius 0.2 m and density 8 × 103 kg m3. Find the moment of inertia about the tangent 3
of its surface. [ π = 3.142] ( July 2017)
7) A meter gauge train is moving at 72 km / hr along a curved railway of radius of curvature 500 m at a certain 3
place. Find the elevation of outer rail above the inner rail so that there is no side pressure on the rail.
[g = 9.8m / s2] ( July. 2018)
8) A solid sphere of diameter 50cm and mass 25 kg rotates about an axis through its centre. Calculate its moment 3
of inertia . If its angular velocity changes from 2 rad/s to 1 rad / sin 5 seconds, calculate the torque applied.
(July 2018)
1) An object of mass 2 kg attached to a wire length 5 m is revolved in a horizontal circle. If it makes 60 r.p.m. find 4
its. ( March 2009)
i) Angular speed ii) Linear iii) Centripetal iv) Centripetal force.
speed acceleration
MECHANICAL PROPERTIES OF FLUID
Theory
1) Define the terms : a) Sphere of influence b) Angle of contact . ( march 2008) 2
2) Define surface tension. State its S.I. unit and dimensions. ( March 2009) 2
3) Draw a neat diagram for the rise of liquid in the capillary tube showing the components of a surface tension. 2
( March 2010 , July 2016)
