Q. No.A ball of mass \(0.15~\text{kg}\) is dropped from a height \(10~\text{m}\), strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is \((g=10 ~\text{m}/\text{s}^2)\) nearly:
1. \(2.1~\text{kg-m/s}\)
2. \(1.4~\text{kg-m/s}\)
3. \(0~\text{kg-m/s}\)
4. \(4.2~\text{kg-m/s}\)
1. \(2.1~\text{kg-m/s}\)
2. \(1.4~\text{kg-m/s}\)
3. \(0~\text{kg-m/s}\)
4. \(4.2~\text{kg-m/s}\)
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 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. \(mg\)
| Assertion (A): | A standing bus suddenly accelerates. If there was no friction between the feet of a passenger and the floor of the bus, the passenger would move back. |
| Reason (R): | In the absence of friction, the floor of the bus would slip forward under the feet of the passenger. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
When a body of mass \(m\) just begins to slide as shown, match List-I with List-II:
| List-I | List-II | ||
| (a) | Normal reaction | (i) | \(P\) |
| (b) | Frictional force (fs) | (ii) | \(Q\) |
| (c) | Weight (mg) | (iii) | \(R\) |
| (d) | mgsin\(\theta ~\) | (iv) | \(S\) |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (ii) | (i) | (iii) | (iv) |
| 2. | (iv) | (ii) | (iii) | (i) |
| 3. | (iv) | (iii) | (ii) | (i) |
| 4. | (ii) | (iii) | (iv) | (i) |
(Consider the surface to be smooth and \(g=10\) ms–2 )
1. \(25\) N
2. \(39\) N
3. \(6\) N
4. \(10\) N
1. \(300\) m
2. \(30\) m
3. \(3\) m
4. \(0.3\) m
| 1. | along south-west | 2. | along eastward |
| 3. | along northward | 4. | along north-east |
| 1. | \(50\) ms-2 | 2. | \(1.2\) ms-2 |
| 3. | \(150\) ms-2 | 4. | \(1.5\) ms-2 |
| 1. | \(10\sqrt3\) | 2. | zero |
| 3. | \(10\) | 4. | \(20\) |
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