A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will:
       
1. decrease by a factor of 2
2. remain constant
3. increase by a factor of 2
4. increase by a factor of 4

Subtopic:  Non Uniform Vertical Circular Motion |
From NCERT
AIPMT - 2011
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A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is µ = 0.5. The distance that the box will move relative to the belt before coming to rest on it, taking g = 10 ms–2 is:

1. 0.4 m 2. 1.2 m
3. 0.6 m 4. Zero
Subtopic:  Friction |
 66%
From NCERT
AIPMT - 2011
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A car of mass \(m\) is moving on a level circular track of radius \(R\). If \(\mu_s\) represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by:
1. \(\sqrt{\frac{Rg}{\mu_s} }\)
2. \(\sqrt{\frac{mRg}{\mu_s}}\)
3. \(\sqrt{\mu_s Rg}\)
4. \(\sqrt{\mu_s m Rg}\)

Subtopic:  Friction |
 87%
From NCERT
AIPMT - 2012
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A car is moving in a circular horizontal track of radius \(10\) m with a constant speed of \(10\) m/s. A bob is suspended from the roof of the car by a light wire of length \(1.0\) m. The angle made by the wire with the vertical is: 
1. \(\pi \over 3 \) 2. \(\pi \over 6\)
3. \(\pi \over 4\) 4. \(0^\circ\)
Subtopic:  Uniform Circular Motion |
 71%
From NCERT
NEET - 2013
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A person holding a rifle (mass of person and rifle together is \(100\) kg) stands on a smooth surface and fires \(10\) shots horizontally, in \(5\) s. Each bullet has a mass of \(10~\mathrm{g}\) with a muzzle velocity of \(800~\mathrm{ms^{-1}}\). The final velocity acquired by the person and the average force exerted on the person are: 
1. \(-0.08 \mathrm{~ms}^{-1} ; 16 \mathrm{~N} \)
2. \(-0.8 \mathrm{~ms}^{-1} ; 16 \mathrm{~N} \)
3. \(-1.6 \mathrm{~ms}^{-1} ; 16 \mathrm{~N} \)
4. \(-1.6 \mathrm{~ms}^{-1} ; 8 \mathrm{~N}\)
Subtopic:  Application of Laws |
 58%
From NCERT
NEET - 2013
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A tube of length \(\text L\) is filled completely with an incompressible liquid of mass \(\text M\) and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is:

1. \(ML \omega^2 \over 2\) 2. \(ML^2 \omega \over 2\)
3. \(ML \omega^2 \) 4. \(ML^2 \omega^2 \over 2\)
Subtopic:  Uniform Circular Motion |
 57%
From NCERT
AIPMT - 2006
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A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of 30° with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is:
              

1. 48 N

2. 24 N

3. 12 N

4. 96 N

Subtopic:  Application of Laws |
 76%
From NCERT
AIPMT - 2006
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A block \(B\) is pushed momentarily along a horizontal surface with an initial velocity \(v.\) If \(\mu\) is the coefficient of sliding friction between \(B\) and the surface, the block \(B\) will come to rest after a time: 
 
1. \(v \over g \mu\)
2. \(g \mu \over v\)
3. \(g \over v\)
4. \(v \over g\)

Subtopic:  Friction |
 79%
From NCERT
AIPMT - 2007
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Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be:
1.  Mv Newton

2.  2Mv Newton

3.  Mv2 Newton

4.  zero

Subtopic:  Newton's Laws |
 66%
From NCERT
AIPMT - 2008
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A roller coaster is designed such that riders experience "weightlessness" as they go around the top of a hill whose radius of curvature is \(20\) m. The speed of the car at the top of the hill is between:
1. \(14\) m/s and \(15\) m/s
2. \(15\) m/s and \(16\) m/s
3. \(16\) m/s and \(17\) m/s
4. \(13\) m/s and \(14\) m/s
Subtopic:  Uniform Circular Motion |
 71%
From NCERT
AIPMT - 2008
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