A block of mass \(m\) is in contact with the cart \((C)\) as shown in the figure.
The coefficient of static friction between the block and the cart is \(\mu.\) The acceleration \(a\) of the cart that will prevent the block from falling satisfies:
1. \(a > \dfrac{mg}{\mu}\)
2. \(a > \dfrac{g}{\mu m}\)
3. \(a \ge \dfrac{g}{\mu}\)
4. \(a < \dfrac{g}{\mu}\)
The coefficient of static friction between the block and the cart is \(\mu.\) The acceleration \(a\) of the cart that will prevent the block from falling satisfies:
1. \(a > \dfrac{mg}{\mu}\)
2. \(a > \dfrac{g}{\mu m}\)
3. \(a \ge \dfrac{g}{\mu}\)
4. \(a < \dfrac{g}{\mu}\)
The mass of a lift is \(2000\) kg. When the tension in the supporting cable is \(28000\) N, then its acceleration is:
(Take \(g=10\) m/s2)
| 1. | \(30\) ms-2 downwards | 2. | \(4\) ms-2 upwards |
| 3. | \(4\) ms-2 downwards | 4. | \(14\) ms-2 upwards |
Two blocks of masses \(2\) kg and \(3\) kg are tied at the ends of a light inextensible string passing over a frictionless pulley as shown.
If the system is accelerating upward with acceleration \(5\) m/s2, the tension in the string is:
1. \(24\) N
2. \(36\) N
3. \(48\) N
4. \(18\)N
A body, under the action of a force \(\overset{\rightarrow}{F} = 6 \hat{i} - 8 \hat{j} + 10 \hat{k}\), acquires an acceleration of 1 ms-2. The mass of this body must be:
1. 2 √10 kg
2. 10 kg
3. 20 kg
4. 10 √2 kg
| 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 |
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. \(v \over g\)
A particle slides down on a smooth incline of inclination , fixed in an elevator going up with an acceleration of 2 m/s2. The box of incline has a length of 4 m. The time taken by the particle to reach the bottom will be:
1. \(\frac89\sqrt3s\)
2. \(\frac98\sqrt3s\)
3. \(\frac43\sqrt{\frac{\sqrt3}{2}}s\)
4. \(\frac34\sqrt{\frac{\sqrt3}{2}}s\)
A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of 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
1. \(60.25^\circ\)
2. \(63.90^\circ\)
3. \(26.12^\circ\)
4. \(30.00^\circ\)
A block of mass \(10~\text{kg}\) is in contact with the inner wall of a hollow cylindrical drum of radius \(1~\text{m}.\) The coefficient of friction between the block and the inner wall of the cylinder is \(0.1.\) The minimum angular velocity needed for the cylinder, which is vertical and rotating about its axis, will be:
\(\left(g= 10~\text{m/s}^2\right )\)
1. \(10~\pi~\text{rad/s}\)
2. \(\sqrt{10}~\pi~\text{rad/s}\)
3. \(\frac{10}{2\pi}~\text{rad/s}\)
4. \(10~\text{rad/s}\)
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