# 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 |
81%
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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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 |
63%
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 |
70%
From NCERT
AIPMT - 1999
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If the kinetic energy of a body is increased by $$300$$%, then the percentage change in momentum will be:
1. $$100$$%
2. $$150$$%
3. $$265$$%
4. $$73.2$$%

Subtopic:  Concept of Work |
74%
From NCERT
AIPMT - 2002
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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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Two springs A and B having spring constant ${K}_{A}$ $and$ ${K}_{B}$  $\left({K}_{A}$ $=$ $2{K}_{B}\right)$ are stretched by applying a force of equal magnitude. If the energy stored in spring A is E, then the energy stored in B will be:

1.  2E

2.  $\frac{E}{4}$

3. $\frac{E}{2}$

4.  4E

Subtopic:  Elastic Potential Energy |
68%
From NCERT
AIPMT - 2001
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