The upper half of an inclined plane with inclination $\phi$ is perfectly smooth, while the lower half is rough. $A$ body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by-

- A
$2 \sin \phi$

- B
$2 \cos \phi$

- C
$2 \tan \phi$

- D
$ \tan \phi$

A bomb of mass $3m$ kg explodes into two pieces of mass $m kg$ and $2m$ $kg$. If the velocity of m kg mass is $16 m/s$, the total kinetic energy released in the explosion is ................. $\mathrm{mJ}$

Two balls at same temperature collide. What is conserved

A ball is thrown from $10\,m$ height at speed $v_0$ vertically downward. In colliding surface of earth it looses $50\%$ of its energy and again reach upto same height. Value of $v_0$ is :- .................$\mathrm{m}/ \mathrm{s}$

A bullet of mass m moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the block will be

A wire, which passes through the hole is a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies on the wire is

- [IIT 2014]