# In a ballistics demonstration, a police officer fires a bullet of mass $$50.0$$ g with speed $$200$$ m/s on soft plywood of thickness $$2.00$$ cm. The bullet emerges with only $$\text{10%}$$ of its initial kinetic energy. The emergent speed of the bullet is: 1. $$0$$ 2. $$53.2$$ m/s 3. $$63.2$$ m/s 4. $$6.32$$ m/s

Subtopic:  Work Energy Theorem |
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A woman pushes a trunk on a railway platform which has a rough surface. She applies a force of $$100$$ N over a distance of $$10$$ m. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to $$50$$ N. The total distance through which the trunk has been moved is $$20$$ m. The plot of force applied by the woman and the frictional force, which is $$50$$ N versus displacement is given below. Work done by the two forces over $$20$$ m are:

 1 $$1750$$ J and $$-1000$$ J 2 $$1750$$ J and $$1000$$ J 3 $$-1750$$ J and $$1000$$ J 4 $$-1750$$ J and $$-1000$$ J
Subtopic:  Work Done by Variable Force |
69%
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A block of mass $$m=1$$ kg, moving on a horizontal surface with speed $$v_i=\mathrm{2~m/s}$$ enters a rough patch ranging from $${x=0.10~\text m}$$ to $${x=2.01~\text m}$$. The retarding force $$F_r$$ on the block in this range is inversely proportional to $$x$$ over this range,

\begin{aligned} {F}_{r} & =\dfrac{-{k}}{x} \text { for } 0.1<{x}<2.01 {~\text{m}} \\ & =0 \quad ~\text { for } {x}<0.1 \text{ m} \text { and } {x}>2.01 \text{ m} \end{aligned}

where $$k=0.5~\text{J}$$. What is the final kinetic energy and speed $$v_f$$ of the block as it crosses this patch?
1. $$5$$ J and $$1$$ m/s
2. $$1$$ J and $$5$$ m/s
3. $$0.5$$ J and $$1$$ m/s
4. $$0.05$$ J and $$2$$ m/s

Subtopic:  Work Energy Theorem |
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A bob of mass $$m$$ is suspended by a light string of length $$L$$. It is imparted a horizontal velocity $$v_{0}$$ at the lowest point $$A$$ such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the horizontal velocity $$v_{0}$$ is:

1. $$\sqrt{5 gl}$$

2. $$\sqrt{4 gl}$$

3. $$\sqrt{3 gl}$$

4. $$\sqrt{gl}$$

Subtopic:  Work Energy Theorem |
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A bob of mass m is suspended by a light string of length $$L.$$ It is imparted a horizontal velocity $$v_0$$ at the lowest point $$A$$ such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, the ratio of the kinetic energies $$\dfrac{K_B}{K_C}$$ ${\mathrm{}}_{}$at points $${B}$$ and $${C}$$ is:

 1 $$1:3$$ 2 $$3:1$$ 3 $$1:5$$ 4 $$5:1$$
Subtopic:  Work Energy Theorem |
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A bob of mass m is suspended by a light string of length $$L$$. It is imparted a horizontal velocity $$v_0$$ at the lowest point $$A$$ such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point $$C$$. If the connecting string is cut at point $$C$$, the trajectory of bob is:

 1 straight line 2 circular 3 projectile 4 can't be determined
Subtopic:  Work Energy Theorem |
63%
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To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $$1000$$ kg moving with a speed $$18.0$$ km/h on a smooth road and colliding with a horizontally mounted spring of spring constant $$6.25\times 10^3~{\mathrm{N/m}}$$. The maximum compression in the spring is:
1. $$3$$ m
2. $$0.2$$ m
3. $$1$$ m
4. $$2$$ m

Subtopic:  Elastic Potential Energy |
72%
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To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $$1000~\text{kg}$$ moving with a speed of $$18~\text{km/h}$$ on a rough road and colliding with a horizontally mounted spring of spring constant $$2.5\times 10^3~\text{N/m}$$If the coefficient of friction between road and tyre of the car, $$\mu$$, to be $$0.375$$. Maximum compression of the spring is:
1. $$3.5~\text{m}$$

2. $$2.0~\text{m}$$
3. $$1.5~\text{m}$$
4. $$2.5~\text{m}$$

Subtopic:  Elastic Potential Energy |
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The values of energy required to break one bond in DNA $$(10^{-20}~\mathrm{J})$$ and the kinetic energy of an air molecule $$(10^{-21}~\mathrm{J})$$ in eV respectively are:

 1 $$0.6$$ eV and $$0.06$$ eV 2 $$0.006$$ eV and $$0.06$$ eV 3 $$0.06$$ eV and $$0.06$$ eV 4 $$0.06$$ eV and $$0.006$$ eV

Subtopic:  Concept of Work |
60%
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An elevator can carry a maximum load of $$1800$$ kg (elevator + passengers) is moving up with a constant speed of $$2$$ m/s. The frictional force opposing the motion is $$4000$$ N. The minimum power delivered by the motor to the elevator is:
1. $$59000$$ W
2. $$44000$$ W
3. $$11000$$ W
4. $$22000$$ W

Subtopic:  Power |
73%
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