$A$ 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?

$A$ simple pendulum is released from $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at $B$ is

$A$ body of mass $2\, kg$ is thrown up vertically with a kinetic energy of $490\, J$. If the acceleration due to gravity is $9.8\, m/s^2$,then the height at which the kinetic energy of the body becomes half its original value is ............ $m$.

The velocity-time graph for a body of mass $10 \ kg$ is shown in the figure. The work done on the body in the first two seconds of motion is:

An unloaded bus can be stopped by applying brakes on a straight road after covering a distance $x$. Suppose the passengers add $50 \%$ of its weight as the load and the braking force remains unchanged,how far will the bus go after the application of the brakes? (Velocity of the bus in both cases is the same.)

$A$ body of mass $6 \,kg$ is acted upon by a force which causes a displacement in it given by $x = \frac{t^2}{4} \,m$, where $t$ is the time in seconds. The work done by the force in $2 \,seconds$ is: (in $\,J$)