$A$ block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$,by a force $F = 20\, N$,making an angle of $30^o$ with the horizontal,as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block,in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$

For the given system,find the tension $T_2$ in the upper string.

What is the value of the contact force $R$ on an object of mass $m$ placed on an inclined plane with angle $\theta$?

$A$ truck starting from rest moves with an acceleration of $5 \ m/s^2$ for $1 \ s$ and then moves with constant velocity. The velocity $v/s$ time graph for the block on the truck with respect to the ground is: (Assume that the block does not fall off the truck and the coefficient of friction $\mu = 0.2$,$g = 10 \ m/s^2$)

Give the magnitude and direction of the net force acting on a stone of mass $0.1\; kg$,
$(a)$ just after it is dropped from the window of a stationary train,
$(b)$ just after it is dropped from the window of a train running at a constant velocity of $36\; km/h$,
$(c)$ just after it is dropped from the window of a train accelerating with $1\; m/s^2$,
$(d)$ lying on the floor of a train which is accelerating with $1\; m/s^2$,the stone being at rest relative to the train.
Neglect air resistance throughout.

$A$ metallic block of mass $20 \ kg$ is dragged with a uniform velocity of $0.5 \ ms^{-1}$ on a horizontal table for $2.1 \ s$. The coefficient of kinetic friction between the block and the table is $0.10$. What will be the maximum possible rise in temperature of the metal block if the specific heat of the block is $0.1 \ cal \ g^{-1} \ ^{\circ}C^{-1}$ (in $^{\circ} C$)? Assume $g = 10 \ ms^{-2}$ and a uniform rise in temperature throughout the whole block. [Ignore absorption of heat by the table]