A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by
A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by
- A
$\frac{{m{v^2}t}}{{{T^2}}}$
- B
$\frac{{m{v^2}{t^2}}}{{{T^2}}}$
- C
$\frac{1}{2}\,\frac{{m{v^2}t}}{{{T^2}}}$
- D
$\frac{1}{2}\,\frac{{m{v^2}{t^2}}}{{{T^2}}}$
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A curved surface is shown in figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$ which is at a slightly greater height than $C$.
With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.
$(a)$ For which balls is total mechanical energy conserved ?
$(b)$ Which ball $(s)$ can reach $D$ ?
$(c)$ For ball which do not reach $D$, which of the balls can reach back $A$ ?
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With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.
$(a)$ For which balls is total mechanical energy conserved ?
$(b)$ Which ball $(s)$ can reach $D$ ?
$(c)$ For ball which do not reach $D$, which of the balls can reach back $A$ ?