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Assertion – Reason type questions : For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. Statement – 1: The periodic time of a simple pendulum increases on the surface of moon. Statement – 2 : Moon is very small as compared to Earth.

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Explanation

“g” in less on moon $ \therefore form the equation T = 2 \pi \sqrt { l^1 \over g} $

T will increase As compared to earth, moon in small

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 For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.

Statement – 1: If the length of a simple pendulum is increased by 3%, then the periodic time changes by 1.5%.

Statement – 2 : Periodic time of a simple pendulum is proportional to its length.

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Explanation

$ periodic \; time \,T \alpha \sqrt l $ $ \therefore \triangle T = {1 \over 2 \sqrt l } . \triangle l\; \{ On differentiation \}$ $ \therefore { \triangle T \over T } = 1.5 \% $

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Assertion – Reason type questions : For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. Statement – 1: For a particle executing S.H.M. with an amplitude of 0.01 m and frequency 30 hz, the maximum acceleration is $36p^2 m/s^2 $. Statement – 2 : The maximum acceleration for the above particle is $ \pm ù2A$, where A is amplitude.

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Explanation

$ a_{max} = \omega^2 A = 4 \pi ^2 f^2 A = 4 \pi^2 (30) ^2 \times 0.01 $ Since the oscillator moves between + A& -A, maximum acceleration $ = \pm 36 \pi^2 $

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Assertion – Reason type questions : For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. Statement – 1 : The periodic time of a stiff spring is less than that of a soft spring. Statement – 2 : The periodic time of a spring depends on its force constant value and for a stiff spring, it is more.

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Explanation

Energy dissipates & so amplitude decreases. Statement -2 in false.

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Assertion – Reason type questions : For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. Statement – 1 : The amplitude of an oscillator decreases with time. Statement – 2 : The frequency of an oscillator decreases with time.

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Explanation

Statement -1 in true. statement -2 in false. In a SHM, amplitude & phase does not depend on restoring force.

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Assertion – Reason type questions : For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. Statement – 1 : For a particle executing SHM, the amplitude and phase is decided by its initial position and initial velocity. Statement – 2 : In a SHM, the amplitude and phase is dependent on the restoring force.

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Explanation

Time taken bythe spring $k_2$ to get maximum compressed from point D= half period of oscillation of the block. (if block in attached at the force end of spring) $ i.e t_2 = { T_2 \over 2 } = { 1 \over 2 } 2 \pi \sqrt {m \over k_2 } = { 1 \over 2 } 2 \pi \sqrt {0.2 \over 0.3 } = { \pi \over 4 } s $

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A block having mass M is placed on a horizontal frictionless surface. This mass is attached to one end of a spring having force constant k. The other end of the spring is attached to a rigid wall. This system consisting of spring and mass M is executing SHM with amplitude A and frequency f. When the block is passing through the mid-point of its path of motion, a body of mass mis placed on top of it, as a result of which its amplitude and frequency changes to A’ and f’. The ratio of frequencies $ { f' \over f } $ =..............................

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Explanation

$ f = {1 \over 2 \pi } \sqrt { k \over M } $ and $ f' = {1 \over 2 \pi } \sqrt { k \over m + M } $

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A block having mass M is placed on a horizontal frictionless surface. This mass is attached to one end of a spring having force constant k. The other end of the spring is attached to a rigid wall. This system consisting of spring and mass M is executing SHM with amplitude A and frequency f. When the block is passing through the mid-point of its path of motion, a body of mass mis placed on top of it, as a result of which its amplitude and frequency changes to A’ and f’. If the velocity before putting the mass and after putting it is $ \nu $ and $ \nu ' $ respectively, then $ { \nu' \over \nu } $=...................................

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Explanation

According to the law of conservation of momentum, $ MV = (M + m) \nu ' $

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A block having mass M is placed on a horizontal frictionless surface. This mass is attached to one end of a spring having force constant k. The other end of the spring is attached to a rigid wall. This system consisting of spring and mass M is executing SHM with amplitude A and frequency f. When the block is passing through the mid-point of its path of motion, a body of mass mis placed on top of it, as a result of which its amplitude and frequency changes to A’ and f’. The ratio of amplitudes $ { A^1 \over A } $ = ........

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Explanation

According to the law of conservation of energy, Kinetic Energy at mid point = potential Energy at the end points $ \therefore { 1 \over 2 } M \nu^2 = { 1 \over 2 } k A^2 $ $ And { 1 \over 2} ( M + m ) \nu ^{1 ^2 } = {1 \over 2 } k A^{1 ^2 } $

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The equation for displacement of a particle at time t is given by the equation y = 3Cos2t + 4Sin2t. . The motion of the particle is …………..

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Explanation

$ y = 3 cos 2t + 4 sin 2 t $ $ \therefore A sin \phi = 3 and A cos \phi = 4 $ $ \therefore y = A sin \phi cos 2 t + A cos \phi sin 2 t $ $ \therefore y = A sin ( \omega t + \phi ) $ Which shows that the motion is simple harmonic motion

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