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

Curve between net forcevs time is shown Initially particle is at rest .. Which of the following best represents the resulting velocity-time graph of the particle ?

A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............

$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by

A spring of spring constant $5 \times 10^3\, N/m$ is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\, cm$ is .............. $\mathrm{N}$  $-$ $\mathrm{m}$

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by