The figure shows the position-time graph of a particle of mass \(4\) kg. What is the force on the particle for \(t>4\) s?  (Consider one-dimensional motion only).

       

1. \(0\) 
2. \(40~\mathrm{N}\) 
3. \(20~\mathrm{N}\) 
4. \(10~\mathrm{N}\)

Subtopic:  Application of Laws |
 81%
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Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m/s collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
1. \(0.4 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)
2. \(0.3 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)
3. \(0.6 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)
4. \(0.7 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)

Subtopic:  Application of Laws |
 79%
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A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s, what is the recoil speed of the gun?
1. \(1.2 \mathrm{~cm} \mathrm{~s}^{-1}\)
2. \(2.2 \mathrm{~cm} \mathrm{~s}^{-1}\)
3. \(2.0 \mathrm{~cm} \mathrm{~s}^{-1}\)
4. \(1.6 \mathrm{~cm} \mathrm{~s}^{-1}\)

Subtopic:  Newton's Laws |
 75%
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A stone of mass 0.25 kg tied to the end of a string is whirled around in a circle of radius 1.5 m with a speed of 40 rev/min in a horizontal plane. The tension in the string is:

1. 5.6 N
2. 6.6 N
3. 3.4 N
4. 4.2 N

Subtopic:  Uniform Circular Motion |
 65%
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The figure shows a man of mass \(65\) kg standing stationary with respect to a horizontal conveyor belt that is accelerating with \(1\) ms-2If the coefficient of static friction between the man’s shoes and the belt is \(0.2,\) up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Take \(g=10\) m/s2)

  
 
1. \(2\) ms-2 2. \(3\) ms-2
3. \(1\) ms-2 4. \(9.8\) ms-2
Subtopic:  Friction |
 67%
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A stone of mass \(\mathrm{m}\) tied to the end of a string revolves in a vertical circle of radius \(\mathrm{R}.\) The net forces at the lowest and highest points of the circle directed vertically downwards are:

Lowest point Highest point
1. \(\mathrm{mg}-\mathrm{T_1}\) \(\mathrm{mg}+\mathrm{T_2}\)
2. \(\mathrm{mg}+\mathrm{T_1}\) \(\mathrm{mg}+\mathrm{T_2}\)
3. mg+T1-mv12R mg-T2+mv22R
4. mg-T1-mv12R mg+T2+mv22R

(T1 and v1 denote the tension and speed at the lowest point.T2 and v2 denote corresponding values at the highest point.)

Subtopic:  Non Uniform Vertical Circular Motion |
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A helicopter of mass 1000 kg rises with a vertical acceleration of 15 ms-2. The crew and the passengers weigh 300 kg. The magnitude and direction of the action of the rotor of the helicopter on the surrounding air are:

1. 3.25×104 N upwards
2. 3.25×104 N downwards
3. 7.5×103 N upwards
4. 7.5×103 N downwards

Subtopic:  Application of Laws |
 54%
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A stream of water flowing horizontally with a speed of \(15\) ms-1 pushes out of a tube of cross-sectional area \(10^{-2}\) m2 and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound? (Density of water, \(\rho=10^{3}\)  kg-m-3)
1. \(1500\) N
2. \(2250\) N
3. \(1650\) N
4. \(2200\) N

Subtopic:  Application of Laws |
 69%
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An aircraft executes a horizontal loop at a speed of \(720\) km/h with its wings banked at \(15^{\circ}\). What is the radius of the loop? (Take \(g=10~\text{m/s}^{2}\)\(\tan 15^{\circ}=0.27\))
1. \(1.30\) km
2. \(14.9\) km
3. \(1.55\) km
4. \(20.9\) km

Subtopic:  Banking of Roads |
 61%
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A train runs along an unbanked circular track of radius \(30\) m at a speed of \(54\) km/h. The mass of the train is \(10^{6}\) kg. What is the angle of banking required to prevent wearing out of the rail?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(53^\circ\)
4. \(37^\circ\)

Subtopic:  Banking of Roads |
 73%
From NCERT
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