# 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 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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A force $$F$$ acting on an object varies with distance $$x$$ as shown below:

The force is in Newton and $$x$$ is in meters. The work done by the force in moving the object from $$x = 0$$ to $$x = 6$$ m is:
1. $$18.0$$ J
2. $$13.5$$ J
3. $$4.5$$ J
4. $$9.0$$ J

Subtopic:  Work Done by Variable Force |
91%
From NCERT
AIPMT - 2005
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A ball is thrown vertically upward. It has a speed of 10m/sec when it has reached one-half of its maximum height. How high does the ball rise? Take g = 10 m/s2:

1. 5m

2. 15m

3. 10 m

4. 20 m

Subtopic:  Work Energy Theorem |
70%
From NCERT
AIPMT - 2005
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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 of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2. Both of them have the same momentum, but their kinetic energies are E1 and E2 respectively. If m1 > m2 then:

1. $\frac{{\mathrm{E}}_{1}}{{\mathrm{E}}_{2}}=\frac{{\mathrm{m}}_{1}}{{\mathrm{m}}_{2}}$

2. ${\mathrm{E}}_{1}>{\mathrm{E}}_{2}$

3. ${\mathrm{E}}_{1}={\mathrm{E}}_{2}$

4. ${\mathrm{E}}_{1}<{\mathrm{E}}_{2}$

Subtopic:  Concept of Work |
72%
From NCERT
AIPMT - 2004
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A stone is tied to a string of length 'l' is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed 'u'. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is:

1. $\sqrt{{u}^{2}-g\ell }$

2. $u-\sqrt{{u}^{2}-2g\ell }$

3.

4. $\sqrt{2\left({\mathrm{u}}^{2}-\mathrm{g}\ell \right)}$

Subtopic:  Work Energy Theorem |
From NCERT
AIPMT - 2004
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A mass of $$0.5$$ kg moving with a speed of $$1.5$$ m/s on a horizontal smooth surface, collides with a nearly weightless spring with force constant $$k=50$$ N/m. The maximum compression of the spring would be:

1. $$0.12$$ m
2. $$1.5$$ m
3. $$0.5$$ m
4. $$0.15$$ m

Subtopic:  Elastic Potential Energy |
80%
From NCERT
AIPMT - 2004
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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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