A moving block having mass $$m$$ collides with another stationary block having a mass of $$4m.$$ The lighter block comes to rest after the collision. When the initial velocity of the lighter block is $$v,$$ then the value of the coefficient of restitution $$(e)$$ will be:
1. $$0.5$$
2. $$0.25$$
3. $$0.8$$
4. $$0.4$$

Subtopic: Â Collisions |
Â 78%
From NCERT
NEET - 2018
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A body initially at rest and sliding along a frictionless track from a height $$h$$ (as shown in the figure) just completes a vertical circle of diameter $$\mathrm{AB}= D.$$ The height $${h}$$ is equal to:

1. $${3\over2}D$$
2. $$D$$
3. $${7\over4}D$$
4. $${5\over4}D$$

Subtopic: Â Gravitational Potential Energy |
Â 71%
From NCERT
NEET - 2018
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Consider a drop of rainwater having a mass of $$1~\text{gm}$$ falling from a height of $$1~\text{km}$$. It hits the ground with a speed of $$50~\text{m/s}$$. Take $$g$$  as constant with a value $$10~\text{m/s}^2.$$ The work done by the
(i) gravitational force and the
(ii) resistive force of air is:

 1 $$(\text{i})~1.25~\text{J};$$ $$(\text{ii})~-8.25~\text{J}$$ 2 $$(\text{i})~100~\text{J};$$ $$(\text{ii})~8.75~\text{J}$$ 3 $$(\text{i})~10~\text{J};$$ $$(\text{ii})~-8.75~\text{J}$$ 4 $$(\text{i})~-10~\text{J};$$ $$(\text{ii})~-8.75~\text{J}$$

Subtopic: Â Work Energy Theorem |
Â 69%
From NCERT
NEET - 2017
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Two identical balls $$\mathrm{A}$$ and $$\mathrm{B}$$ having velocities of $$0.5~\text{m/s}$$ and $$-0.3~\text{m/s}$$ respectively collide elastically in one dimension. The velocities of $$\mathrm{B}$$ and $$\mathrm{A}$$ after the collision respectively will be:
1. $$-0.5 ~\text{m/s}~\text{and}~0.3~\text{m/s}$$
2. $$0.5 ~\text{m/s}~\text{and}~-0.3~\text{m/s}$$
3. $$-0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}$$
4. $$0.3 ~\text{m/s}~\text{and}~0.5~\text{m/s}$$

Subtopic: Â Collisions |
Â 57%
From NCERT
NEET - 2016
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A body of mass 1 kg begins to move under the action of a time dependent force $$F = 2 t$$ $$\hat{i} + 3 t^{2}\ \hat{j}$$ N, where $$\hat{i}$$ and $$\hat{j}$$ are unit vectors along X and Y axis, What power will be developed by the force at the time (t) ?

(a) $$\left(2 t^{2} + 4 t^{4}\right) W$$

(b) $$\left(2 t^{3} + 3 t^{4}\right) W$$

(c) $$\left(2 t^{3} + 3 t^{5}\right) W$$

(d) $$\left(2 t + 3 t^{3}\right) W$$

Subtopic: Â Power |
Â 68%
From NCERT
NEET - 2016
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What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

(1) $\sqrt{2\mathrm{gR}}$

(2) $\sqrt{3gR}$

(3) $\sqrt{5gR}$

(4) $\sqrt{gR}$

Subtopic: Â Work Energy Theorem |
Â 77%
From NCERT
NEET - 2016
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A bullet of mass $$10$$ g moving horizontal with a velocity of $$400$$ m/s strikes a wood block of mass $$2$$ kg which is suspended by light inextensible string of length $$5$$ m. As a result, the centre of gravity of the block is found to rise a vertical distance of $$10$$ cm. The speed of the bullet after it emerges horizontally from the block will be:

 1 $$100$$ m/s 2 $$80$$ m/s 3 $$120$$ m/s 4 $$160$$ m/s
Subtopic: Â Collisions |
Â 59%
From NCERT
NEET - 2016
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Two identical balls $$A$$ and $$B$$ having velocities of $$0.5~\text{m/s}$$ and $$-0.3~\text{m/s}$$, respectively, collide elastically in one dimension. The velocities of $$B$$ and $$A$$ after the collision, respectively, will be:

 1 $$-0.5~\text{m/s}~\text{and}~0.3~\text{m/s}$$ 2 $$0.5~\text{m/s}~\text{and}~-0.3~\text{m/s}$$ 3 $$-0.3~\text{m/s}~\text{and}~0.5~\text{m/s}$$ 4 $$0.3~\text{m/s}~\text{and}~0.5~\text{m/s}$$
Subtopic: Â Collisions |
Â 61%
From NCERT
NEET - 2016
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A body of mass $$1$$ kg begins to move under the action of a time-dependent force $$\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right)$$ N, where $$\hat{i}$$ and $$\hat{j}$$ are unit vectors along the $$\mathrm{X}$$ and $$\mathrm{Y}$$-axis. What power will be developed by the force at the time ($$t$$)?
1. $$\left(2 t^2+4 t^4\right)$$ W
2. $$\left(2 t^3+3 t^3\right)$$ W
3. $$\left(2 t^3+3 t^5\right)$$ W
4. $$\left(2 t^3+3 t^4\right)$$ W
Subtopic: Â Power |
Â 79%
From NCERT
NEET - 2016
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What is the minimum velocity with which a body of mass $$m$$ must enter a vertical loop of radius $$R$$ so that it can complete the loop?
1. $$\sqrt{2 g R}$$
2. $$\sqrt{3 g R}$$
3. $$\sqrt{5 g R}$$
4. $$\sqrt{ g R}$$

Subtopic: Â Gravitational Potential Energy |
Â 85%
From NCERT
NEET - 2016
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