The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$. What is the ratio $${l \over R}$$ such that the moment of inertia is minimum?

A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:

A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its initial speed is v₀ = 10 ms^–1. If, after 10 s, its energy is $${1 \over 8}mv_0^2$$, the value of k will be:

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?