Embibe Experts Solutions for Chapter: Work, Energy and Power, Exercise 4: BEGINNER'S BOX - 4

Two springs have their respective force constants $K_1$ and $K_2$. Both are stretched till their elastic potential energies are equal. If the stretching forces are $F_1$ and $F_2$ find $\frac{F_1}{F_2}$.

A long spring is stretched by $1 \mathrm{cm}$. If work done in this process is $W$, then find out the work done in further stretching it by $1 \mathrm{cm}$.

A $20 \mathrm{N}$ stone falls accidentally from a height of $4 \mathrm{m}$ on to a spring of stiffness constant $1960 \mathrm{N} {\mathrm{m}}^{-1}$. Write down the equation to find out the maximum compression $\left(x_m\right)$ of the spring.

A block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of the spring constant?

A block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in the figure. The block is displaced by $x$ towards the right and released. The velocity of the block when it is at $\frac{x}{2}$ will be

A pump on the ground floor of a building can pump up water to fill a tank of volume $30 {\mathrm{m}}^3$ in $15 \min$. If the tank is $40 \mathrm{m}$ above the ground, and the efficiency of the pump is $30\%$, how much electric power is consumed by the pump?

An engine pumps up $100 \mathrm{kg}$ of water through a height of $10 \mathrm{m}$ in $5 \mathrm{s}$. If the efficiency of the engine is $60\%$, find out the power of the engine ($g=10 \mathrm{m} {\mathrm{s}}^{-2}$).