$A$ person is managing to be at rest between two vertical walls by pressing one wall with his hands and feet and the second wall with his back. The coefficient of friction is $0.5$ between his body and the walls. If the force with which the person pushes the walls is $500 \ N$,then the mass of the person is (Take $g = 10 \ m \ s^{-2}$) (in $kg$)

In the arrangement shown in the figure,if the blocks of masses $m$ and $2m$ are released from rest,find the tension in the string. (Given: $\mu_1 = 2/3$ for mass $m$,$\mu_2 = 1/3$ for mass $2m$,the string is massless and inextensible,and the pulley is frictionless.)

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,then choose the correct statement$(s)$.

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,and if $a_{min}$ and $a_{max}$ are the minimum and maximum values of $a_0$ for which the blocks remain stationary with respect to the surface,then identify the correct statements.

$A$ man pulls a block heavier than himself with a light horizontal rope. The coefficient of friction is the same between the man and the ground,and between the block and the ground.

$A$ body of mass $3 \, kg$ hits a wall at an angle of $60^\circ$ with the wall and returns at the same angle. The speed of the body is $10 \, m/s$ and the impact time is $0.2 \, s$. Calculate the force exerted on the wall.