A basket and its contents have mass $M$. A monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3$ seconds. How fast is the basket rising at the end of the $3$ seconds? Neglect the mass of the pulley and the rope. (given : $g = 32ft/s^2$)

A body of mass $1\, kg$ is thrown upwards with a velocity $20\, m/s$. It momentarily comes to rest after attaining a height of $18\, m$. How much energy is lost due to air friction ............. $\mathrm{J}$  $(g = 10\, m/s^2)$

A force $\vec F = (5\hat i + 3\hat j)\;N$is applied over a particle which displaces it from its original position to the point $\vec s = (2\hat i - 1\hat j)$m. The work done on the particle is.........$J$

A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ $meter$ as shown in figure. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ............. $\mathrm{m}/ \mathrm{s}$

A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

In the figure shown the potential energy $(U)$ of a particle is plotted against its position $'x'$ from origin. The particle at