A block of mass $2\, kg$ is placed on a rough inclined plane as shown in the figure $(\mu = 0.2)$ so that it just touches the spring. The block is allowed to move downwards. The spring will be compressed to a maximum of .............. $\mathrm{cm}$
$0.1$
$6.6 $
$1 $
$13$
A uniform chain of mass $m$ and length $L$ is originally placed mid-way on the top of a fixed smooth double-sided wedge (Figure- $A$). The length of each side of the wedge is $L$ . It is then given a slight push. The kinetic energy of the chain when the whole chain has just slid to the left side of the wedge (Figure- $B$), is :
$A$ small bucket of mass $M\, kg$ is attached to $a$ long inextensible cord of length $L\, m$ . The bucket is released from rest when the cord is in a horizontal position. At its lowest position, the bucket scoops up $m\, kg$ of water and swings up to a height $h$. The height $h$ in meters is
A particle of mass $m$ slides from rest down a plane inclined at $30^o$ to the horizontal. The force of resistance acting on the particle during motion is $ms^2$ where $s$ is the displacement of the particle from its initial position. The velocity (in $m/s$) of the particle when $s = 1\,m$ is $v$. The value of $\frac{3v^2}{14}$ is :-
A particle is released from a height $H$. At a certain height its kinetic energy is two times its potential energy. Height and speed of particle at that instant are
A particle is projected vertically upwards with a speed of $16\ m/s$ , after some time , when it again passes through the point of projection, its speed is found to be $8\ m/s$ . It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height attained by the particle is ...................... $\mathrm{m}$ ( $g$ = $10\ m/s^2$ )