Question banks

A solid cylinder of mass 20 kg and radius 0.25 m rotates about its own axis. Find its moment of inertia and its radius of gyration.

On a velocity-time graph, what do the slope and the area under the curve each represent, and why is the area a displacement rather than a distance?

A body falls from rest. Show that the distances it covers in successive equal intervals of time are in the ratio 1 : 3 : 5 : 7.

A car's stopping distance at 15 m/s is 20 m. Assuming the same braking deceleration, estimate its stopping distance at 30 m/s, and explain the reasoning.

Why was the kilogram redefined in 2018, and what is it now based on?

Both K = (1/2)mv^2 and K = (3/16)mv^2 have the dimensions of energy. Explain why dimensional analysis cannot decide between them, and name two other things it cannot do.

Add 436.32 g, 227.2 g and 0.301 g, giving the answer to the correct precision. Why is the rule different from multiplication?

Check whether v^2 = u^2 + 2as is dimensionally correct.

How many significant figures are in 0.005060?

A cube's side is measured as 7.203 m. Give its total surface area and volume to the correct number of significant figures.

The period of a pendulum T depends on length l, mass m of the bob, and g. Derive the relation using dimensional analysis, and state what the method cannot give you.

Find the dimensions of the universal gravitational constant G from F = G m1 m2 / r^2.

Why is g zero at the centre of the Earth?

If Earth's period is 1 year at radius R, find the period of a planet at radius 4R.

Calculate the escape velocity on the Moon (g = 1.62 m/s^2, R = 1740 km).

Find the orbital velocity of a satellite at 300 km height (R = 6400 km, M = 6e24 kg).

Find g at a height equal to R above Earth's surface.

A solid sphere rolls down a 10 m high incline. Find its speed at the bottom (g = 10 m/s^2).

A diver with I = 15 kg m^2 spins at 3 rad/s tucked, then straightens to I = 25 kg m^2. Find the new angular velocity.

A torque of 10 N m acts on a body with I = 5 kg m^2 for 4 s from rest. Find the angular velocity attained.

A disc has I = (1/2)MR^2 about its central perpendicular axis. Find I about a parallel axis at the rim.

Masses 2 kg and 3 kg are at (1,0) and (4,0) m. Find the centre of mass.

Can kinetic energy be negative? Can potential energy be negative?

In an elastic collision a 2 kg ball at 4 m/s hits a 4 kg ball at rest. Find the final velocities.