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Question

For the spring block arrangement as shown in figure:


Given that k1=2k2. If force applied by the first spring on the block is F1 and force applied by the second spring on the block is F2, choose the correct option(s) if the block is in equilibrium with the action of an external force 30 N on the block.

A
x1=2x2
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B
x1=x2
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C
F1=F2=30 N
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D
F1=20 N,F2=10 N
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Solution

The correct options are
B x1=x2
D F1=20 N,F2=10 N
Let 1st spring be stretched by distance x1 and 2nd spring be stretched by distance x2
Both springs are connected in parallel, x1=x2
Applying equilibrium condition on block gives,
F1+F2=F(1)
Now,
F1=k1x1
F2=k2x2

From (1) 30=k1x1+k2x2
[k1=2k2]
30=3k2x2=3F2
F2=10 N

F1=k1x1=2k2x2=2F2
F1=2×10=20 N

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