A light spring of length $20\, cm$ and force constant $2\, kg/cm$ is placed vertically on a table. A small block of mass $1\, kg$. falls on it. The length $h$ from the surface of the table at which the ball will have the maximum velocity is ............... $\mathrm{cm}$
$20$
$15$
$10$
$5$
A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Identify the correct statement $(s)$ related to the situation when the particle starts moving downward.
Write the equation of total mechanical energy of a body having mass $m$ and stationary at height $H$.
The potential energy function for a particle executing linear simple harmonic motion is given by $V(x)=$ $k x^{2} / 2,$ where $k$ is the force constant of the oscillator. For $k=0.5\; N m ^{-1}$ the graph of $V(x)$ versus $x$ is shown in Figure. Show that a particle of total energy $1 \;J$ moving under this potential must 'turn back" when it reaches $x=\pm 2 m$
A man is standing on a cart of mass double the mass of man. Initially cart is at rest. Now man jumps horizontally with relative velocity $'u'$ with respect to cart. Then work done by internal forces of the man during the process of jumping will be :
Three balls, $A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures, one kept on the ground and the other at height $h$, from the ground as shown in the figure. They take time $t_A$ and $t_B$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$, vertically above $X$ and reaches $X$ in time $t_C$. Choose the correct option.