1. A sphere fits inside a cube.
The length of the cube and the diameter of the sphere are 10.0±0.2cm.
What is the ratio (percentage uncertainty of the volume of the sphere/percentage uncertainty of the volume of the cube)?
2. A swimming pool contains 18 × 106 kg of pure water. The molar mass of water is 18 g mol–1.What is the correct estimate of the number of water molecules in the swimming pool?
3. An aircraft is moving horizontally. A parachutist leaves the aircraft and a few seconds later opens her parachute. Which graph shows the variation of the vertical speed v with time t for the parachutist from the time she leaves the aircraft until just before landing?
4. An object of mass m rests on a horizontal plane. The angle θ that the plane makes with the horizontal is slowly increased from zero. When θ = θ0, the object begins to slide. What are the coefficient of static friction μs and the normal reaction force N of the plane at θ = θ0?
5. A stone is falling at a constant velocity vertically down a tube filled with oil. Which of the following statements about the energy changes of the stone during its motion are correct?
- I. The gain in kinetic energy is less than the loss in gravitational potential energy.
- II. The sum of kinetic and gravitational potential energy of the stone is constant.
- III. The work done by the force of gravity has the same magnitude as the work done by friction.
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
6. A spring of negligible mass and length l0 hangs from a fixed point. When a mass m is attached to the free end of the spring, the length of the spring increases to l. The tension in the spring is equal to k Δx, where k is a constant and Δx is the extension of the spring. What is k?
C.mg/l − l0
7. A ball with mass m moves horizontally with speed u. The ball hits a vertical wall and rebounds in the opposite direction with speed v < u. The duration of the collision is T. What are the magnitude of the average force exerted by the wall on the ball and the loss of kinetic energy of the ball?
8. A train on a straight horizontal track moves from rest at constant acceleration. The horizontal forces on the train are the engine force and a resistive force which increases with speed. Which graph represents the variation with time t of the power P developed by the engine?
9. The graph shows how the acceleration a of an object varies with distance travelled x.
The mass of the object is 3.0 kg. What is the total work done on the object?
A. 300 J
B. 400 J
C. 1200 J
D. 1500 J
10. A substance is heated at constant power. The graph shows how the temperature T of the substance varies with time t as the state of the substance changes from liquid to gas.
What can be determined from the graph?
A. The specific heat capacity of the gas is smaller than the specific heat capacity of the liquid.
B. The specific heat capacity of the gas is larger than the specific heat capacity of the liquid.
C. The specific latent heat of fusion of the substance is less than its specific latent heat of vaporization.
D. The specific latent heat of fusion of the substance is larger than its specific latent heat of vaporization.
11. Which of the following is not an assumption of the kinetic model of ideal gases?
A. All particles in the gas have the same mass.
B. All particles in the gas have the same speed.
C. The duration of collisions between particles is very short.
D. Collisions with the walls of the container are elastic.