A car of mass \(1000\) kg negotiates a banked curve of radius \(90\) m on a frictionless road. If the banking angle is of \(45^\circ,\) the speed of the car is:
1. | \(20\) ms–1 | 2. | \(30\) ms–1 |
3. | \(5\) ms–1 | 4. | \(10\) ms–1 |
A body of mass \(M\) hits normally a rigid wall with velocity \(v\) and bounces back with the same velocity. The impulse experienced by the body is:
1. \(1.5Mv\)
2. \(2Mv\)
3. zero
4. \(Mv\)
A block of mass \(\mathrm{m}\) is in contact with the cart C as shown in the figure.
The coefficient of static friction between the block and the cart is . The acceleration of the cart that will prevent the block from falling satisfies:
1.
2.
3.
4.
A gramophone record is revolving with an angular velocity . A coin is placed at a distance r from the centre of the record. The static coefficient of friction is . The coin will revolve with the record if:
1.
2.
3.
4.
An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, the first part 1 kg moving with a velocity of 12 and the second part 2 kg moving with a velocity of 8 . If the third part flies off with a velocity of 4 , its mass would be:
1. 5 kg
2. 7 kg
3. 17 kg
4. 3 kg
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 |
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 |
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. Newton
4. zero