Three different objects of mass $m_1$, $m_2$ and $m_3$ are allowed to fall from rest and from the same point 'O' along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of:

A $100 \text{ g}$ iron ball having velocity $10 \text{ m/s}$ collides with a wall at an angle $30^\circ$ and rebounds with the same angle. If the period of contact between the ball and wall is $0.1 \text{ second}$, then the force experienced by the wall is:

An object of mass $500 \text{ g}$ initially at rest is acted upon by a variable force whose $x$-component varies with $x$ in the manner shown. The velocities of the object at the points $x=8 \text{ m}$ and $x=12 \text{ m}$ would have the respective values of nearly:

When a body moves with a constant speed along a circle

Force $F$ on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12$ m is:

A particle moves with a velocity $(5\hat i-3\hat j+6\hat k)\text{ ms}^{-1}$ horizontally under the action of a constant force $(10\hat i+10\hat j+20\hat k)\text{ N}$. The instantaneous power supplied to the particle is:

In a circus stuntman rides a motorbike in a circular track of radius $R$ in the vertical plane. The minimum speed at highest point of track will be:

The minimum work done in pulling up a block of wood weighing $2 \text{ kN}$ for a length of $10 \text{ m}$ on a smooth plane inclined at an angle of $15^\circ$ with the horizontal is (given $\sin 15^\circ = 0.2588$):

A man fires a bullet of mass $200 \text{ g}$ at a speed of $5 \text{ m/s}$. The gun is of one kg mass. By what velocity the gun rebounds backwards?