A particle, initially at rest on a frictionless horizontal surface, is acted upon by a horizontal force which is constant in size and direction. A graph is plotted between the work done $(W) $ on the particle, against the speed of the particle, $(v)$. If there are no other horizontal forces acting on the particle the graph would look like
A body of $\mathrm{m} \mathrm{kg}$ slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is:
(given, $\mathrm{R}=14 \mathrm{~m}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2$ and $\sqrt{2}=1.4$ )
In a ballistics demonstration a police officer fires a bullet of mass $50.0 \;g$ with speed $200 \;m s ^{-1}$ on soft plywood of thickness $2.00 \;cm .$ The bullet emerges with only $10 \%$ of its initial kinetic energy. What is the emergent speed of the bullet?
$A$ 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 stone with weight $w$ is thrown vertically upward into the air from ground level with initial speed $v_0$. If a constant force $f$ due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is
A bullet of mass $200\,g$ having initial kinetic energy $90\,J$ is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to $40\,J$ within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is $.....m$