A block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of spring constant ?
$\frac{3mv^2}{4x^2}$
$\frac{mv^2}{4x^2}$
$\frac{mv^2}{2x^2}$
$\frac{2mv^2}{x^2}$
A bullet looses ${\left( {\frac{1}{n}} \right)^{th}}$ of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be
A block of mass $m=1\; kg$. moving on a horizontal surface with speed $v_{t}=2 \;m s ^{-1}$ enters a rough patch ranging from $x=0.10\; m$ to $x=2.01\; m .$ The retarding force $F$ on the block in this range is inversely proportional to $x$ over this range,
$F_{r}=\frac{-k}{x}$ for $0.1 < x < 2.01 \;m$
$=0$ for $x < 0.1\; m$ and $x > 2.01\; m$
where $k=0.5\; J .$ What is the final kinetic energy and speed $v_{f}$ of the block as it crosses this patch ?
A body of mass $8\,kg$ is moved by a force $F = 3x\,N,$ where $x$ is the distance covered. Initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s.$ The final speed is ........... $m/s$
A $1000\,\, kg$ elevator rises from rest in the basement to the fourth floor, a distance of $20\,\, m$. As it passes the fourth floor its speed is $4\,m/sec$. There is a constant frictional force of $500\, N$. The work done by the lifting mechanism is
If $250 \,J$ of work is done in sliding a $5 \,kg$ block up an inclined plane of height $4 \,m$. value of Work done against friction is ............. $J$ $\left(g=10 \,ms ^{-2}\right)$