Statement I: | If the acceleration of a particle is directed towards a fixed point, and proportional to the distance from that point – the motion is SHM. |
Statement II: | During SHM, the kinetic energy of the particle oscillates at twice the frequency of the SHM. |
1. | Statement I is incorrect and Statement II is correct. |
2. | Both Statement I and Statement II are correct. |
3. | Both Statement I and Statement II are incorrect. |
4. | Statement I is correct and Statement II is incorrect. |
List-I | List-II |
(a) motion with constant speed | (i) SHM |
(b) motion with constant acceleration | (ii) uniform circular motion |
(c) oscillatory motion | (iii) projectile motion |
(d) random motion | (iv) molecular motion in gas |
1. | a - (iv), b - (ii), c - (iii), d - (i) |
2. | a - (i), b - (iii), c - (ii), d - (iv) |
3. | a - (ii), b - (iii), c - (i), d - (iv) |
4. | a - (ii), b - (iii), c - (iv), d - (i) |
Statement I: | A graph of its acceleration vs displacement (from mean position) is a straight line. |
Statement II: | A graph of its velocity vs displacement (from mean position) is an ellipse. |
1. | Statement I is incorrect and Statement II is correct. |
2. | Both Statement I and Statement II are correct. |
3. | Both Statement I and Statement II are incorrect. |
4. | Statement I is correct and Statement II is incorrect. |
Assertion (A): | The graph between velocity and displacement for a simple harmonic motion is an ellipse. |
Reason (R): | Velocity does not change uniformly with displacement in simple harmonic motion. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
Assertion (A): | Water in a U-tube executes SHM. The time period for mercury-filled up to the same height in the U-tube is greater than that in the case of water. |
Reason (R): | The amplitude of an oscillating pendulum goes on increasing. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
Assertion (A): | If the bob of a simple pendulum is kept in a horizontal electric field, its period of oscillation will remain the same. |
Reason (R): | If bob is charged and kept in a horizontal electric field, then the time period will be decreased. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | (A) is False but (R) is True. |
1. | 2. | ||
3. | 4. |
A body oscillates with SHM according to the equation (in SI units), x = 5 cos [2π t + π/4]. At t = 1.5 s, acceleration of the body will be:
1. | \(140 \mathrm{~cm} / \mathrm{s}^2 \) | 2. | \(160 \mathrm{~m} / \mathrm{s}^2 \) |
3. | \(140 \mathrm{~m} / \mathrm{s}^2 \) | 4. | \(14 \mathrm{~m} / \mathrm{s}^2\) |
The potential energy of a simple harmonic oscillator, when the particle is halfway to its endpoint, will be:
1. \(\frac{2E}{3}\)
2. \(\frac{E}{8}\)
3. \(\frac{E}{4}\)
4. \(\frac{E}{2}\)
A particle of mass m oscillates with simple harmonic motion between points x1 and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph:
1. | 2. | ||
3. | 4. |