A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is
A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is
- A
$mg(h - d) + \frac{1}{2}K{d^2}$
- B
$mg(h + d) + \frac{1}{2}K{d^2}$
- C
$mg(h + d) - \frac{1}{2}K{d^2}$
- D
$mg(h - d) - \frac{1}{2}K{d^2}$
Similar Questions
Answer carefully, with reasons :
$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?
$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?
$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?
$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?
(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).
Answer carefully, with reasons :
$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?
$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?
$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?
$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?
(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).
In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $\mathrm{ergs}$
In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $\mathrm{ergs}$
When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$
When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$
A ball $P$ collides with another identical ball $Q$ at rest. For what value of coefficient of restitution $e$, the velocity of ball $Q$ become two times that of ball $P$ after collision
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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 .............. $\mathrm{m} / \mathrm{s}$