$A$ block of mass $5\,kg$ starting from rest is pulled up on a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal with an effective acceleration of $1\,m/s^2$. The power delivered by the pulling force at $t = 10\,s$ from the start is $.....\,W$. [Use $g = 10\,m/s^2$] (calculate the nearest integer value).

Two identical balls are connected by a massless and inextensible thread of length $L$. The system is in gravity-free space with the thread just taut. At $t = 0$,each ball is imparted a velocity $v$; one ball is given a velocity towards the other ball,and the other is given a velocity perpendicular to the first. Then,

$A$ block of mass $M = 100 \, kg$ is pulled by a force $T$ at an angle of $37^{\circ}$ with the horizontal. The coefficient of friction between the block and the ground is $\mu = 1/3$. $A$ person of mass $m = 25 \, kg$ is standing on a platform and pulls the block with the force $T$. Find the maximum upward acceleration $a_{\max}$ of the person such that the block just starts to move.

Block $A$ of mass $m$ and block $B$ of mass $M$ are connected by a massless spring over a pulley on a rough plane with coefficient of friction $\mu$. $A$ force $F$ is applied on block $A$ to the left. Find the minimum value of $M$ to move the block $A$ towards the right.

The figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with $1 \; m/s^2$. What is the net force on the man? If the coefficient of static friction between the man's shoes and the belt is $0.2$,up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man $= 65 \; kg.)$

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. When the downward acceleration of the elevator becomes equal to $g$,then