Work Done, Varying Force and Path

Q. The force exerted by a compression device is given by $F\left(x\right)=kx(x-l)$, where $l$ is the maximum possible compression, $x$ is the compression and $k$ is a constant. The work required to compress the device by a distance $d$ will be maximum when

1. $d=\frac{l}{4}$
2. $d=\frac{l}{\sqrt{2}}$
3. $d=\frac{l}{2}$
4. $d=l$

Q. A bullet of mass ${10}^{-3}\text{kg}$ strikes an obstacle and moves at ${60}^{\circ }$ to its original direction. If its speed also changes from $20\text{m/s}$ to $10\text{m/s}$. Find the magnitude of impulse acting on the bullet.

1. $\sqrt{5}\times {10}^{-2}\text{Ns}$
   
2. $\sqrt{3}\times {10}^{-2}\text{Ns}$
   
3. $\sqrt{2}\times {10}^{-2}\text{Ns}$
   
4. $2\times {10}^{-2}\text{Ns}$

Q.

A body of mass 3 kg is under a force, which causes a displacement in it is given by $S=\frac{t^3}{3}$ (in m). Find the work done by the force in first 2 seconds

1. 2 J

2. 3.8 J

3. 5.2 J

4. 24 J

Q. The force exerted by a compression device is given by $F\left(x\right)=kx(x-l)$, where $l$ is the maximum possible compression, $x$ is the compression and $k$ is a constant. The work required to compress the device by a distance $d$ will be maximum when

1. $d=\frac{l}{4}$
2. $d=\frac{l}{\sqrt{2}}$
3. $d=\frac{l}{2}$
4. $d=l$

Q. A block of $10\text{kg}$ is pulled in a vertical plane along a frictionless surface in the form of an arc of a circle of radius $10\text{m}$. A force of $200\text{N}$ is applied such that tension in the string always remains along the tangential direction as shown in figure. If the block started from rest at $A$, the velocity at $B$ would be:
Consider $\frac{\pi }{3}=1$ for calculation and take $g=10{\text{m/s}}^2$)

1. $10\sqrt{3}\text{m/s}$
2. $10\text{m/s}$
3. $\frac{5}{\sqrt{3}}\text{m/s}$
4. $3\sqrt{3}\text{m/s}$

Q. A bullet is fired from a gun. The force on the bullet is given by F = 600 - 2 $\times$ ${10}^5$ t, where F is in Newton and t in seconds. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet

1. 9 Ns
2. Zero
3. 0.9 Ns
4. 1.8 Ns

Q. A block of $10\text{kg}$ is pulled in a vertical plane along a frictionless surface in the form of an arc of a circle of radius $10\text{m}$. A force of $200\text{N}$ is applied such that tension in the string always remains along the tangential direction as shown in figure. If the block started from rest at $A$, the velocity at $B$ would be:
Consider $\frac{\pi }{3}=1$ for calculation and take $g=10{\text{m/s}}^2$)

1. $10\sqrt{3}\text{m/s}$
2. $10\text{m/s}$
3. $\frac{5}{\sqrt{3}}\text{m/s}$
4. $3\sqrt{3}\text{m/s}$