Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by
Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by
- A
$\frac{1}{2}\,m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
- B
$m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
- C
$\frac{1}{2}\,{\left( {\frac{{mv}}{{{t_1}}}} \right)^2}{\kern 1pt} {t^2}$
- D
$\frac{1}{2}\,m\,\frac{v^2}{{{t^2_1}}}{\kern 1pt} {t^2}$
Similar Questions
A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is .............. $\mathrm{m} / \mathrm{s}$
A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is .............. $\mathrm{m} / \mathrm{s}$
A particle is made to move from the origin in three spells of equal distances, first along the $x-$ axis, second parallel to $y-$ axis and third parallel to $z-$ axis. One of the forces acting on it is has constant magnitude of $50\,N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal and total work done in all the three spells is $300\,J$. The final coordinates of the particle will be
A particle is made to move from the origin in three spells of equal distances, first along the $x-$ axis, second parallel to $y-$ axis and third parallel to $z-$ axis. One of the forces acting on it is has constant magnitude of $50\,N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal and total work done in all the three spells is $300\,J$. The final coordinates of the particle will be
A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$ along the inclined calculate
$(a)$ work done against gravity
$(b)$ work done against force of friction
$(c)$ increases in potential energy
$(d)$ increases in kinetic energy
$(e)$ work done by applied force
A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$ along the inclined calculate
$(a)$ work done against gravity
$(b)$ work done against force of friction
$(c)$ increases in potential energy
$(d)$ increases in kinetic energy
$(e)$ work done by applied force
The kinetic energy $K$ of a particle moving along a circle of radius $R$ depends upon the distance $s$ as $K = as^2$. The force acting on the particle is
The kinetic energy $K$ of a particle moving along a circle of radius $R$ depends upon the distance $s$ as $K = as^2$. The force acting on the particle is
A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, work required to pull the hanging part on to the table is
A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, work required to pull the hanging part on to the table is