Q. No.Two bodies of mass, \(4~\text{kg}\) and \(6~\text{kg}\), are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (\(g\)) is:
1.
\(\frac{g}{2}\)
2.
\(\frac{g}{5}\)
3.
\(\frac{g}{10}\)
4.
\(g\)
A point mass \(m\) is moved in a vertical circle of radius \(r\) with the help of a string. The velocity of the mass is at the lowest point. The tension in the string at the lowest point is:
1. \(6mg\)
2. \(7mg\)
3. \(8mg\)
4. \(mg\)
Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is \(0.05\).
( \(g=10 \mathrm{~m} / \mathrm{s}^2\), mass of the string is negligible and no other friction exists ).
1. \( 1.25 \mathrm{~m} / \mathrm{s}^2 \)
2. \( 1.50 \mathrm{~m} / \mathrm{s}^2 \)
3. \( 1.66 \mathrm{~m} / \mathrm{s}^2 \)
4. \( 1.00 \mathrm{~m} / \mathrm{s}^2\)
A body of mass \(m\) is kept on a rough horizontal surface (coefficient of friction =\(\mu)\). A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by \(\vec F\) where:
1. \(|{\vec F}| = mg+\mu mg\)
2. \(|\vec F| =\mu mg\)
3. \(|\vec F| \le mg\sqrt{1+\mu^2}\)
4. \(|\vec F| = mg\)
A truck is stationary and has a bob suspended by a light string in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of \(a.\) In the frame of the truck, the pendulum will tilt:
| 1. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{sin}^{-1} \left( \frac{a}{g} \right )\) |
| 2. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{cos}^{-1} \left ( \frac{a}{g} \right )\) |
| 3. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \frac{a}{g} \right )\) |
| 4. | to the left and the angle of inclination of the pendulum with the vertical is \(\text{tan}^{-1} \left ( \frac{g}{a} \right )\) |
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. \(\sqrt{\mu_s m Rg}\)
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 |
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
Two masses as shown are suspended from a massless pulley. What would be the acceleration of the system when masses are left free?
1. \(2g/3\)
2. \(g/3\)
3. \(g/9\)
4. \(g/7\)
(where \(g\) is the acceleration due to gravity.)
A body of mass 3 kg hits a wall at an angle of 60º & returns at the same angle. The impact time was 0.2 s. Calculate the force exerted on the wall.
1. 150 N
2. 50 N
3. 100 N
4. 75 N
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