$A$ bullet moving with a velocity of $100\, m/s$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet,when the velocity is doubled,will be

$A$ bead of mass $m$ slides without friction on the wall of a vertical circular hoop of radius $R$ as shown in the figure. The bead moves under the combined action of gravity and a massless spring of constant $k$ attached to the bottom of the hoop. The natural (equilibrium) length of the spring is $R$. If the bead is released from the top of the hoop with negligible initial speed,what is the velocity of the bead when the length of the spring becomes $R$? ($g$ is the acceleration due to gravity)

$A$ block of mass $m$ starts at rest at height $h$ on a frictionless inclined plane. The block slides down the plane,travels across a rough horizontal surface with coefficient of kinetic friction $\mu$,and compresses a spring with force constant $k$ a distance $x$ before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface,sliding up the plane. The block travels a total distance $d$ on the rough horizontal surface. The correct expression for the maximum height $h'$ that the block reaches on its return is

The figure below shows a small mass connected to a string,which is attached to a vertical post. If the ball is released when the string is horizontal as shown below,the magnitude of the total acceleration (including radial and tangential) of the mass as a function of the angle $\theta$ is

$A$ large block of wood of mass $M = 5.99 \, kg$ is hanging from two long massless cords. $A$ bullet of mass $m = 10 \, g$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards,their centre of mass rising a vertical distance $h = 9.8 \, cm$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take $g = 9.8 \, ms^{-2}$) (in $m/s$)

$A$ particle of mass $m$ is at rest in a train moving with constant velocity with respect to the ground. Now,the particle is accelerated by a constant force $F_0$ acting along the direction of motion of the train for time $t_0$. $A$ girl in the train and a boy on the ground measure the work done by this force. Which of the following are $INCORRECT$?