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. E1E2=m1m2

2. E1>E2

3. E1=E2

4. E1<E2

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. u2g

2. uu22g

3. 2 g

4. 2(u2g)

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 (KA = 2 KB), 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 KA and KB  (KA = 2KB) 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.  E4

3. E2

4.  4E

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