# 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 |
61%
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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 |
74%
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In a nuclear reactor, a neutron of high speed (typically $$\left(10\right)^{7}$$ m/s) must be slowed to $$\left(10\right)^{3}$$ m/s so that it can have a high probability of interacting with isotope $$^{235}_{92}U$$ and causing it to fission. The material making up the light nuclei, usually heavy water $$\left(D_{2} O\right)$$ 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.  $$\dfrac{1}{9}$$

2.  $$\dfrac{8}{9}$$

3.  $$\dfrac{9}{8}$$

4.  $$\dfrac{1}{8}$$

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 $$m_{1} = m_{2}$$. 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 $$\left(\theta\right)_{2}=37^\circ$$. Assume that the collision is elastic and that friction and rotational motion are not important. $$\left(\theta\right)_{1}$$ is:

1. $$53^{o}$$

2. $$0^{o}$$

3. $$37^{o}$$

4. $$30^{o}$$

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The value of the daily intake of a human adult  in kilocalories is:

1.   24 k cal

2.   2.4 kcal

3.   2400 kcal

4.   240 kcal

Subtopic:  Concept of Work |
69%
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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 $$18.0~\text{km/h}$$ on a smooth road and colliding with a horizontally mounted spring of spring constant $$6.25\times 10^3~{\text{N/m}}$$. The maximum compression in the spring is:
1. $$3~\text{m}$$
2. $$0.2~\text{m}$$
3. $$1~\text{m}$$
4. $$2~\text{m}$$
Subtopic:  Elastic Potential Energy |
73%
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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 |
64%
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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 |
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 $$v_{0}$$ 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 |
66%
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