A block of mass $m$ is placed on a rough rotating disc at a distance $r$ from the center. The coefficient of static friction is $\mu_s$. What is the maximum angular speed $\omega$ for which the block will not slip?

A {}_\;^{238}U nucleus decays by emitting an alpha particle of speed $v\;m{s^{ - 1}}$. The recoil speed of the residual nucleus is (in $m{s^{ - 1}}$)

A stationary body of mass 3 kg explodes into three equal pieces. Two of the pieces fly off in two mutually perpendicular directions, one with velocity of $3\;\hat i\;{\rm{m}}{{\rm{s}}^{ - 1}}$ and the other with a velocity of $4\;\hat j\,{\rm{m}}{{\rm{s}}^{ - 1}}$ . If the explosion occurs in ${10^{ - 4}}$ s, the force acting on the third piece in newtons is

A stationary bomb explodes into two parts of masses 3kg and 1kg. The total KE of the two parts after explosion is 2400 J. The KE of smaller part is

A bullet of mass 0.02 kg travelling horizontally with velocity $250\;m{s^{ - 1}}$ strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of 40m. The coefficient of sliding friction of the rough surface is $\left( {g = 9.8\;m{s^{ - 2}}} \right)$

A boy of mass 0.25 kg is projected with muzzle velocity $100\;m{s^{ - 1}}$ from a tank of mass 100 kg. What is the recoil velocity of the tank

Friction always acts in a direction _______ to the direction of motion.

If a block is placed on a rough inclined plane and the angle of inclination is gradually increased, at what angle does the block start sliding if the coefficient of static friction is 0.6?

A bag of mass M hangs by a long thread and a bullet (mass m) comes horizontally with velocity $v$ and gets caught in the bag. For the combined system of bag and bullet, the correct option is

A 5 kg stationary bomb is exploded in three parts having mass $1:1:3$ respectively. Parts having same mass move in perpendicular directions with velocity 39 $\;{\rm{m}}{{\rm{s}}^{ - 1}}$, then the velocity of bigger part will be

A bullet hits and gets embedded in a solid block resting on a frictionless surface .In this process which one of the following is correct?