When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of \(60^\circ\) with horizontal, it can travel a distance \(x_1\) along the plane. But when the inclination is decreased to \(30^\circ\) and the same object is shot with the same velocity, it can travel \(x_2\) distance. Then \(x_1:x_2\) will be:
1. \(1:2\sqrt{3}\)
2. \(1:\sqrt{2}\)
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{3}\)

Subtopic:  Conservation of Mechanical Energy |
 73%
From NCERT
NEET - 2019
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A force \(F = (20 + 10 y)\) acts on a particle in the \(y\)-direction where \(F\) is in Newton and \(y\) is in meter. Work done by this force to move the particle from \(y =0\) to \(y =1\) m is:
1. \(20~\text{J}\)
2. \(30~\text{J}\)
3. \(5~\text{J}\)
4. \(25~\text{J}\)
Subtopic:  Work Done by Variable Force |
 74%
From NCERT
NEET - 2019
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A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

1. inclined at an angle of \(60^{\circ}\) from vertical.
2. the mass is at the highest point.
3. the wire is horizontal.
4. the mass is at the lowest point.
Subtopic:  Gravitational Potential Energy |
 71%
From NCERT
NEET - 2019
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Body \(\mathrm{A}\) of mass \(4m\) moving with speed \(u\) collides with another body \(\mathrm{B}\) of mass \(2m\) at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body \(\mathrm{A}\) is:
1. \(\dfrac{5}{9}\)
2. \(\dfrac{1}{9}\)
3. \(\dfrac{8}{9}\)
4. \(\dfrac{4}{9}\)

Subtopic:  Collisions |
 64%
From NCERT
NEET - 2019
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\(300 ~\text{J}\) of work is done in sliding a \(2~\text{kg}\) block up an inclined plane of height \(10~\text{m}\). Taking \(g=\) \(10\) m/s2, work done against friction is:
1. \(200 ~\text{J}\)
2. \(100 ~\text{J}\)
3. \(\text{zero}\)
4. \(1000 ~\text{J}\)

Subtopic:  Work Done by Variable Force |
 71%
From NCERT
AIPMT - 2006
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A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = 13 t2, where t is in sec. Work done by the force in 2 sec is:

1. 519J

2. 38J

3. 83J

4. 195J

Subtopic:  Work Done by Variable Force |
 77%
From NCERT
AIPMT - 2006
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The potential energy of a long spring when stretched by \(2\) cm is \(U\). If the spring is stretched by \(8\) cm, the potential energy stored in it is:
1. \(4U\)
2. \(8U\)
3. \(16U\)
4. \(U/4\)

Subtopic:  Elastic Potential Energy |
 78%
From NCERT
AIPMT - 2006
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A vertical spring with a force constant \(k\) is fixed on a table. A ball of mass \(m\) at a height \(h\) above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance \(d\). The net work done in the process is:
1. \(mg(h+d)+\frac{1}{2}kd^2\)
2. \(mg(h+d)-\frac{1}{2}kd^2\)
3. \(mg(h-d)-\frac{1}{2}kd^2\)
4. \(mg(h-d)+\frac{1}{2}kd^2\)

Subtopic:  Elastic Potential Energy |
 64%
From NCERT
AIPMT - 2007
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A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is:

1. 100 ms-1

2. 80 ms-1

3. 40 ms-1

4. 120 ms-1

Subtopic:  Collisions |
 57%
From NCERT
AIPMT - 2008
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Water falls from a height of 60 m at a rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine? (g = 10 m/s2)

1. 8.1 kW
2. 10.2 kW
3. 12.3 kW
4. 7.0 kW
Subtopic:  Power |
 81%
From NCERT
AIPMT - 2008
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