Q. No.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
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. \(10~\text{rad/s}\)
A particle moving with velocity \(\vec{v}\) is acted by three forces shown by the vector triangle \(\mathrm{PQR}.\) The velocity of the particle will:
| 1. | change according to the smallest force \(\mathrm{\overrightarrow{Q R}}\) |
| 2. | increase |
| 3. | decrease |
| 4. | remain constant |
A mass m1, placed on top of a trolley of mass m3, is connected to another mass m2 by means of string passing over a smooth pulley as shown in figure. The friction between surfaces is negligible. For m1 ans m2 not to move with respect to trolley, the horizontal force F to be applied on trolley is
1. F=m3g
2. F=(m1 + m2)g
3.
4. F= m1g
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