Mechanics Mock Tests

A road is banked at an angle θ for a curve of radius R. The coefficient of static friction between tyres and road is μ. The maximum safe speed on this curve is (take g = acceleration due to gravity):

An artificial satellite orbits Earth in an elliptical path with perigee distance r_p and apogee distance r_a. If the speed at perigee is v_p, the speed at apogee v_a equals:

A body of mass 4 kg moving at 6 m/s collides elastically with a stationary body of mass 2 kg. After collision, the velocity of the 4 kg body is:

A uniform rod of length L and mass M is pivoted at one end. A bullet of mass m traveling perpendicular to the rod with speed v strikes the other end and embeds. The maximum angle the rod swings to is:

A force of 10 N acts on a body of mass 2 kg initially at rest. The work done in 5 seconds is:

Two planets of masses m₁ and m₂ orbit each other in circular orbits with separation d. The total angular momentum of the system about their center of mass is proportional to:

A force of 10 N acts on a body of mass 2 kg for 3 seconds. The change in momentum of the body is:

The slant side of a frictionless incline making an angle 60° with the vertical is 1 m. Starting from rest the time taken by a mass to slide down the incline from top to the base is: (g = 10 m/s²)