A car is moving with uniform speed on a banked road inclined at an angle $heta$. The coefficient of static friction between the tyres and road is $\mu_s$. What is the maximum speed with which the car can negotiate the curve without skidding, if the radius of the curve is $R$?

A bullet of mass $m$ leaves a gun of mass M kept on a smooth horizontal surface. If the speed of the bullet relative to the gun is v, the recoil speed of the gun will be

A shell at rest at the origin explodes into three fragments of masses 1 kg,2kg and m kg. The 1 kg and 2 kg pieces fly off with speeds off $5m{s^{ - 1}}$ along x-axis and $6m{s^{ - 1}}$ along y-axis respectively. If the m kg piece files off with a speed of $6.5\,m{s^{ - 1}}$, the total mass of the shell must be

A particle is projected with 200 $\;{\rm{m}}{{\rm{s}}^{ - 1}}$, at an angle of ${60^0}$. At the highest point it explodes into three particles of equal masses. One goes vertically upward with velocity 100 $m{s^{ - 1}}$, the second particle goes vertically downward with the same velocity as the first. Then what is the velocity of the third particle?

An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are $2p\hat i\,and\,p\hat j$. The momentum of the third part

A body moving with a velocity v, breaks up into two equal parts. One of the part retraces back with velocity v.Then, the velocity of the other part is

A stone is dropped from a height h. It hits the ground with a certain momentum p. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

A bomb at rest explodes into 3 parts of the same mass. The momentum of the 2 parts is $- 2p\,\hat i\,and\,\hat p j$. The momentum of the third part will have a magnitude of

A shell of mass 10 kg is moving with a velocity of $10\;{\rm{m}}{{\rm{s}}^{ - 1}}$ when it blasts and forms two parts of mass 9 kg and 1 kg respectively. If the 1st mass is stationary, the velocity of the 2nd is

A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with a velocity of

Two balls of masses ${m_1}\,and\,{m_2}$ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass ${m_1}$ travels a distance ${s_1}$ and stops. If the coefficients of friction between the balls and ground are same, the mass $\,{m_2}$ stops after traveling the distance