An object is thrown vertically upward with an initial velocity of $4 \ m/s$. At what height (in $m$) will its kinetic energy be halved?

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

The mass of a pendulum bob is $50 \ gm$. The bob is released from a horizontal position $A$ as shown in the figure. If the length of the pendulum is $1.5 \ m$,what will be its kinetic energy when it reaches the lowest point $B$ of its path? (Take $g = 10 \ m/s^2$)

$A$ force $\overrightarrow{F} = 4 \hat{i} - 15 \hat{j} \text{ N}$ acts on a body, resulting in a displacement of $\overrightarrow{S} = 6 \hat{i} \text{ m}$. If the body had a kinetic energy of $7 \text{ J}$ at the beginning of the displacement, what is the kinetic energy at the end of the displacement (in $\text{ J}$)?

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given, moment of inertia of sphere $= \frac{2}{5} mr^2$].

$A$ bob of a pendulum of length $0.5 \ m$ has a speed of $6 \ ms^{-1}$ at its lowest point. Find the speed of the bob when the string of the pendulum makes $60^{\circ}$ with the vertical. (Take $g=10 \ ms^{-2}$)