If $x$ $=$ $3$ $-4{t}^{2}$ $+$ ${t}^{3}$, then work done in the first 4s will be:
(Mass of the particle is 3 gram)
1.  384 mJ
2.  168 mJ
3.  192 mJ
4.  None of the above

Subtopic:  Work Energy Theorem |
53%
From NCERT
AIPMT - 1998
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Two identical balls A and B are moving with velocity $+0.5$ $m{s}^{-1}$ and $-0.3$ $m{s}^{-1}$ respectively. If they collide head on elastically, then their velocities after collision will be:

1. $-0.3$ $m{s}^{-1}$ $and$ $0.5$ $m{s}^{-1}$

2. $+0.5$ $m{s}^{-1}$ $and$ $+$ $0.3$ $m{s}^{-1}$

3. $-0.4$ $m{s}^{-1}$ $and$ $0.3$ $m{s}^{-1}$

4. $-0.3$ $m{s}^{-1}$ $and$ $-0.4$ $m{s}^{-1}$

Subtopic:  Collisions |
89%
From NCERT
AIPMT - 1998
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A ball is dropped from a height of $$5$$ m. If it rebounds up to a height of $$1.8$$ m, then the ratio of velocities of the ball after and before the rebound will be:
1. $\frac{3}{5}$

2. $\frac{2}{5}$

3. $\frac{1}{5}$

4. $\frac{4}{5}$

Subtopic:  Conservation of Mechanical Energy |
74%
From NCERT
AIPMT - 1998
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The kinetic energy of a person is just half of the kinetic energy of a boy whose mass is just half of that person. If the person increases his speed by $$1~\text{m/s},$$ then his ​​​​​​​kinetic energy equals to that of the boy, then the initial speed of the person was:
1. $$\left( \sqrt{2}+1 \right)~\text{m/s}$$
2. $$\left( 2+\sqrt{2} \right)~\text{m/s}$$
3. $$2\left( 2+\sqrt{2} \right)~\text{m/s}$$
4. none of the above

Subtopic:  Concept of Work |
55%
From NCERT
AIPMT - 1999
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A particle projected with velocity 'u' makes an angle θ with respect to horizontal. Now it breaks in two identical parts at highest point of trajectory. If one part retraces its path, then velocity of the other part is:
1. 3u cos θ
2. 2u cos θ
3. u cos θ
4. u

Subtopic:  Collisions |
From NCERT
AIPMT - 1999
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If two springs, A and B $\left({K}_{A}$ $=$ $2$ ${K}_{B}\right),$ are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:
1.  1 : 2
2.  2 : 1
3.  1 : 1
4.  1 : 4

Subtopic:  Elastic Potential Energy |
62%
From NCERT
AIPMT - 1999
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When a spring is subjected to 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

Subtopic:  Elastic Potential Energy |
69%
From NCERT
AIPMT - 1999
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The bob of a simple pendulum having length l, is displaced from the mean position to an angular position θ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. $\sqrt{2gl\left(1-\mathrm{cos}\theta \right)}$

2. $\sqrt{2gl\left(1+\mathrm{cos}}$ $\theta \right)$

3. $\sqrt{2gl}$ $\mathrm{cos}\theta$

4. $\sqrt{2gl}$

Subtopic:  Work Energy Theorem |
79%
From NCERT
AIPMT - 2000
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If $$\vec{F} = (60\hat{i} + 15\hat{j}-3\hat{k})$$ N and $$\vec{v} = (2\hat{i} - 4\hat{j}+5\hat{k})$$ m/s, then instantaneous power is:
1. $$195$$ watt
2. $$45$$ watt
3. $$75$$ watt
4. $$100$$ watt

Subtopic:  Power |
87%
From NCERT
AIPMT - 2000
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A child is sitting on a swing. Its minimum and maximum heights from the ground are $$0.75$$ m and $$2$$ m, respectively. Its maximum speed will be: (Take $$g=10$$ m/s2)
1. $$10$$ m/s
2. $$5$$ m/s
3. $$8$$ m/s
4. $$15$$ m/s

Subtopic:  Work Energy Theorem |
75%
From NCERT
AIPMT - 2001
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