Work Done, Varying Force and Path

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

Q. A spring of spring constant $5\times {10}^3\text{N/m}$ is stretched initially by $5cm$ from the unstretched position. The work required to further stretch the spring by another $5cm$ is

1. $6.25\text{J}$
2. $12.50\text{J}$
3. $18.75\text{J}$
4. $25.00\text{J}$

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. An objects of mass $40kg$ having velocity $4\hat{i}m/s$ collides with another object of mass $60kg$ having velocity $2\hat{i}m/s$. If collision is pefectly inelastic, then the loss of mechanical energy is

1. $24J$
2. $96J$
3. $48J$
4. $6J$

Q. A force $F=-K(y\hat{i}-x\hat{j})$, (where $K$ is a positive constant) acts on a particle moving in the $XY-$plane. Starting from the origin, the particle is taken along the positive $X-$axis to the plane $(a,0)$ and then parallel to the $Y-$axis to the point $(a,a)$. The total work done by the force $F$ on the particle is

1. $-2K{a}^2$
2. $2K{a}^2$
3. $-K{a}^2$
4. $K{a}^2$

Q. Assertion :A person working on a horizontal road with a load on his head does no work. Reason: No work is said to be done, if directions of force and displacement of load are perpendicular to each other.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Consider a force $\overrightarrow{F}=-x\hat{i}+y\hat{j}$. The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment is?
(all quantities are in SI units)

1. $1$
2. $\frac{3}{2}$
3. $2$
4. $\frac{1}{2}$

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. $3\sqrt{3}\text{m/s}$