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Class 11thPhysics OscillationsOscillationsPhysics

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. New amplitude of oscillation will be:

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>A</mi> <mroot> <mrow> <mfrac> <mrow> <mi>M</mi> </mrow> <mrow> <mi>M</mi> <mo>−</mo> <mi>m</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>A</mi> <mroot> <mrow> <mfrac> <mrow> <mi>M</mi> </mrow> <mrow> <mi>M</mi> <mo>+</mo> <mi>m</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>A</mi> <mroot> <mrow> <mfrac> <mrow> <mi>M</mi> <mo>−</mo> <mi>m</mi> </mrow> <mrow> <mi>M</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>A</mi> <mroot> <mrow> <mfrac> <mrow> <mi>M</mi> <mo>+</mo> <mi>m</mi> </mrow> <mrow> <mi>M</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
3 Views|Posted 4 months ago
Asked by Shiksha User
1 Answer
V
4 months ago
Correct Option - 2
Detailed Solution:

Velocity of block in equilibrium, in first case,

v = A ω = A . k M

Velocity of block in equilibrium, is second case,

v ' = A ' ω ' = A ' k M + m

From conservation of momentum,

Mv = (M + m) v'

⇒ M A k M = ( M + m ) A ' k M + m ⇒ A ' = A M M + m

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