$A$ pendulum bob has a speed $4 \,m/s$ at its lowest position. The pendulum is $1 \,m$ long. When the length of the string makes an angle of $60^{\circ}$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $g=10 \,m/s^2, \cos 60^{\circ}=0.5$).

$A$ sphere is suspended by a thread of length $\ell$. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension point?

$A$ body falls freely from a height $h$ in a gravitational field. Match the following:

Column-$I$	Column-$II$
$(1)$ Potential Energy $=$ Kinetic Energy	$(a)$ At height $\frac{2h}{3}$
$(2)$ Potential Energy $= 2 \times$ Kinetic Energy	$(b)$ Constant at every point
	$(c)$ At height $\frac{h}{2}$

$A$ body of mass $3 \text{ kg}$ is moving under the action of a force which causes a displacement of $\left(\frac{t^3}{3}\right) \text{ m}$, where '$t$' is time in seconds. The work done by the force in the first $2 \text{ seconds}$ is: (in $\text{ J}$)

$A$ 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 ............. $m/s$.

$A$ block of mass $\sqrt{2} \, kg$ is released from the top of an inclined smooth surface as shown in the figure. If the spring constant of the spring is $100 \, N/m$ and the block comes to rest after compressing the spring by $1 \, m$,then the total distance travelled by the block along the incline before it comes to rest is ......... $m$.