Figure shows a boy on a horizontal platform $A$ on a smooth horizontal surface, holding a rope attached to a box $B$ . Boy pulls the rope with a constant force of $50\ N$ . (boy does not slip over the platform). The combined mass of platform $A$ and boy is $250\ kg$ and that of box $B$ is $500\ kg$ . The velocity of $A$ relative to the box $B$ , $5\ s$ after the boy on $A$ begins to pull the rope, will be ............ $m/s$
$1$
$1.5$
$2$
$0.5$
In the arrangement shown in fig. the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $U$. Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed.
Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.
In the figure shown the velocity of lift is $2\,m / s$ while string is winding on the motor shaft with velocity $2\,m / s$ and block $A$ is moving downwards with a velocity of $2\,m / s$, then find out the velocity of block $B -$
Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction, as shown in figure. If the trolley is accelerated horizontally along the positive $x$ -axis with $a_0$, then 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
Two particles $A$ and $B$ are connected by rigid rod $A B$. The rod slides along perpendicular rails as shown here. The velocity of $A$ to the left is $10\; m / s$. What is the velocity of $B$(in $m/s$) when angle $\alpha=60^{\circ}$?