A particle of mass $m$, initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T$. It begins to move with a velocity $u$ after the force stops acting. $F$ is shown in the graph as a function of time. The curve is a semicircle.
$u = \frac{{\pi F_0^2}}{{2m}}$
$u = \frac{{\pi {T^2}}}{{8m}}$
$u = \frac{{\pi {F_0}T}}{{4m}}$
$u = \frac{{{F_0}T}}{{2m}}$
A gun applies a force $F$ on a bullet which is given by $F =\left(100-0.5 \times 10^{5} t \right) N$. The bullet emerges out with speed $400 \,m / s$. Then find out the impulse exerted till force on bullet becomes zero. (in $N - s$)
A strange cat with a mass $m_c$ is sitting at rest on the left plank of a pair of identical planks. Each plank has mass $m_s$ and they rest on frictionless ice. Suddenly, the cat leaps to the right plank, traveling with a horizontal speed $v_{cg}$ measured with respect to the ground. The instant the cat reaches the right plank, it turns around and leaps back to the left plank. The horizontal component of the cat’s speed is again $v_{cg}$ measured with respect to the ground. The final speed of right plank in terms of the masses of the cat and planks and the cat’s leaping speed is (The cat remains on the left plank after its return).
A body of mass $m$ collides against a wall with a velocity $v$ and rebounds with the same speed. Its change of momentum is
A man is at rest in the middle of a pond on perfectly smooth ice. He can get himself to the shore by making use of Newton's
A particle is acted upon by a force whose component's variations with time are shown in diagrams. Then the magnitude of change in momentum of the particle in $0.1\,\,sec$ will be :-