2
1© OCR 2025 Y431/01 Jun25
, 3
Particles A and B move towards each other on a smooth horizontal surface. Particle A has speed
3 m s-1 and particle B has speed 8 m s-1.
After they collide directly, A and B move away from each other, A with a speed of 5.2 m s-1 and B
with a speed of v m s-1 . The collision between A and B is perfectly elastic.
(a) Find the value of v. [1]
(b) State the kinetic energy lost in the collision between A and B. [1]
Two different particles, C and D, move on a smooth horizontal surface. Particle C has a speed of
6.4 m s-1 towards D and particle D has a speed of 1.9 m s-1 away from C.
After they collide directly, the particles move away from each other. The speed of C after the
collision is 0.2 m s-1 . The coefficient of restitution between C and D is 0.8.
You are given that the mass of C is 3.5 kg.
(c) Determine the mass of D. [4]
© OCR 2025 Y431/01 Jun25 Turn over
, 4
2 (a) (i) State the dimensions of force. [1]
(ii) State the dimensions of energy. [1]
The surface tension, S, of a liquid can be defined as force per unit length. It can also be defined as
energy per unit area.
(a) Show that these two definitions of surface tension are dimensionally consistent with one
another. [2]
When a droplet of liquid is placed on a non-absorbent horizontal surface, the maximum height h m
of the droplet is modelled by the formula
h = mSa gb tc ,
where
• m is a dimensionless constant,
• S is the surface tension of the liquid in Nm–1,
• g is the acceleration due to gravity in ms–2,
• t is the density of the liquid in kg m–3.
(b) Use dimensional analysis to determine the values of a , b and c . [4]
At room temperature, water has a density of 1 g cm-3 and a surface tension of 0.073 N m-1 . When
a small droplet of water is placed on a non-absorbent horizontal surface, it has maximum height
0.53 cm.
(c) Find the value of m . [2]
© OCR 2025 Y431/01 Jun25
1© OCR 2025 Y431/01 Jun25
, 3
Particles A and B move towards each other on a smooth horizontal surface. Particle A has speed
3 m s-1 and particle B has speed 8 m s-1.
After they collide directly, A and B move away from each other, A with a speed of 5.2 m s-1 and B
with a speed of v m s-1 . The collision between A and B is perfectly elastic.
(a) Find the value of v. [1]
(b) State the kinetic energy lost in the collision between A and B. [1]
Two different particles, C and D, move on a smooth horizontal surface. Particle C has a speed of
6.4 m s-1 towards D and particle D has a speed of 1.9 m s-1 away from C.
After they collide directly, the particles move away from each other. The speed of C after the
collision is 0.2 m s-1 . The coefficient of restitution between C and D is 0.8.
You are given that the mass of C is 3.5 kg.
(c) Determine the mass of D. [4]
© OCR 2025 Y431/01 Jun25 Turn over
, 4
2 (a) (i) State the dimensions of force. [1]
(ii) State the dimensions of energy. [1]
The surface tension, S, of a liquid can be defined as force per unit length. It can also be defined as
energy per unit area.
(a) Show that these two definitions of surface tension are dimensionally consistent with one
another. [2]
When a droplet of liquid is placed on a non-absorbent horizontal surface, the maximum height h m
of the droplet is modelled by the formula
h = mSa gb tc ,
where
• m is a dimensionless constant,
• S is the surface tension of the liquid in Nm–1,
• g is the acceleration due to gravity in ms–2,
• t is the density of the liquid in kg m–3.
(b) Use dimensional analysis to determine the values of a , b and c . [4]
At room temperature, water has a density of 1 g cm-3 and a surface tension of 0.073 N m-1 . When
a small droplet of water is placed on a non-absorbent horizontal surface, it has maximum height
0.53 cm.
(c) Find the value of m . [2]
© OCR 2025 Y431/01 Jun25
