Two springs, each of spring constant k, are attached to a block of mass m as shown in the figure. The block can slide smoothly along a horizontal platform clamped to the opposite walls of the trolley of mass M. If the block is displaced by x cm and released, the period of oscillation is:
A
T = 2 π 
B
T = 2 π 
C
T = 2 π 
D
T = 2 π 
Text Solution
Verified by ExpertsThe correct answer is:
C
Let displacement of block is x 1 and of cart is x 2 as shown
by linear momentum conservation
mv 1 = Mv 2
⇒ v 2 = 
so x 2 = 
For block Force equation can be written as
F = 2k(x 1 + x 2 ) = mꞷ 2 x 1
⇒ 2k 
= mꞷ 2 x 1
⇒ ꞷ 2 = 2k 
So T = 2 π 
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