Assertion (A): | The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola. |
Reason (R): | Potential energy and kinetic energy do not vary linearly with position. |
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. |
List-I (\(x \text{-}y\) graphs) |
List-II (Situations) |
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(a) | (i) | Total mechanical energy is conserved | |
(b) | (ii) | Bob of a pendulum is oscillating under negligible air friction | |
(c) | (iii) | Restoring force of a spring | |
(d) | (iv) | Bob of a pendulum is oscillating along with air friction |
(a) | (b) | (c) | (d) | |
1. | (iv) | (ii) | (iii) | (i) |
2. | (iv) | (iii) | (ii) | (i) |
3. | (i) | (iv) | (iii) | (ii) |
4. | (iii) | (ii) | (i) | (iv) |
A body is performing SHM, then its:
(a) | average total energy per cycle is equal to its maximum kinetic energy. |
(b) | average kinetic energy per cycle is equal to half of its maximum kinetic energy. |
(c) | mean velocity for a complete cycle is equal to \(\dfrac{2}{\pi}\) times of its maximum velocity. |
(d) | root mean square velocity is \(\dfrac{1}{\sqrt{2}}\) times of its maximum velocity. |
Choose the correct alternatives:
1. (a), (b), (d)
2. (a), (c)
3. (b), (d)
4. (b), (c), (d)
For a particle executing SHM the displacement \(x \) is given by, \(A\cos \omega t.\) Identify the graph which represents the variation of potential energy (P.E.) as a function of time \(t\) and displacement \(x.\)
1. I, III
2. II, IV
3. II, III
4. I, IV