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 $$\mathrm{x=0.10~m}$$ to $$\mathrm{x=2.01~m}$$. The retarding force $$F_r$$ on the block in this range is inversely proportional to $$x$$ over this range, \begin{aligned} \mathrm{F}_{\mathrm{r}} & =\frac{-\mathrm{k}}{\mathrm{x}} \text { for } 0.1<\mathrm{x}<2.01 \mathrm{~m} \\ & =0 \quad \text { for } \mathrm{x}<0.1 \mathrm{~m} \text { and } \mathrm{x}>2.01 \mathrm{~m} \end{aligned} where $$k=0.5~\mathrm{J}$$. 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 ${\mathrm{v}}_{0}$ 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 ${\mathrm{v}}_{0}$ is:

1.   $\sqrt{5\mathrm{gl}}$

2.   $\sqrt{4\mathrm{gl}}$

3.  $\sqrt{3\mathrm{gl}}$

4.   $\sqrt{\mathrm{gl}}$

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 $$\frac{K_B}{K_C}$$ ${\mathrm{}}_{}$at points $$\mathrm{B}$$ and $$\mathrm{C}$$ is:
${\mathrm{}}_{}$

1. $$1:3$$
2. $$3:1$$
3. $$1:5$$
4. $$5:1$$

Subtopic:  Work Energy Theorem |
77%
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A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity ${\mathrm{v}}_{0}$ 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. 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 kg moving with a speed of 18.0 km/h on a rough road and colliding with a horizontally mounted spring of spring constant If the coefficient of friction between road and tyre of the car, µ, to be 0.375. Maximum compression of the spring is:

1.   3.5 m

2.   2.0 m

3.   1.5 m

4.   2.5 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 |
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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 |
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In a nuclear reactor, a neutron of high speed (typically ${10}^{7}$ m/s) must be slowed to ${10}^{3}$ m/s so that it can have a high probability of interacting with isotope ${}_{92}{}^{235}\mathrm{U}$ and causing it to fission. The material making up the light nuclei, usually heavy water $\left({\mathrm{D}}_{2}\mathrm{O}\right)$ or graphite, is called a moderator. Find the fraction of the kinetic energy of the neutron lost by it in an elastic collision with light nuclei like deuterium.

1.  $\frac{1}{9}$

2.  $\frac{8}{9}$

3.  $\frac{9}{8}$

4.  $\frac{1}{8}$

Subtopic:  Work Energy Theorem |
67%
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Consider the collision depicted in the figure below to be between two billiard balls with equal masses . The first ball is called the cue while the second ball is called the target. The billiard player wants to ‘sink’ the target ball in a corner pocket, which is at an angle ${\mathrm{\theta }}_{2}$ 37°. Assume that the collision is elastic and that friction and rotational motion are not important. ${\mathrm{\theta }}_{1}$ is:

1.  ${53}^{\mathrm{ο}}$

2.  ${0}^{\mathrm{ο}}$

3.  ${37}^{\mathrm{ο}}$

4.  ${30}^{\mathrm{ο}}$

67%
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