A boy holds a uniform chain of length $2\,m$ which is kept on a smooth table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table .............. $\mathrm{J}$
$7.2$
$3.6$
$120$
$1200$
A particle moves with a velocity $\vec v\, = \,5\hat i - 3\hat j + 6\hat k\,\,m/s$ under the influence of a constant force $\vec F\, = \,10\hat i + 10\hat j + 20\hat k$. Instantaenous power will be ............... $\mathrm{J} / \mathrm{s}$
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 $A$ ?
A body of mass $1\, kg$ is thrown upwards with a velocity $20\, m/s$. It momentarily comes to rest after attaining a height of $18\, m$. How much energy is lost due to air friction ............. $\mathrm{J}$ $(g = 10\, m/s^2)$
When a constant force is applied to a body moving with constant acceleration, power does not remain constant. For power to be constant, the force has to vary with speed as follows
How much work does a pulling force of $40\, N$ do on the $20\, kg$ box in pulling it $8\, m$ across the smooth floor at a constant speed. The pulling force is directed at $60^o$ above the horizontal .............. $\mathrm{J}$