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Question

A block of mass 2 kg is attached to a spring of force constant k=10 N/m as shown in the figure. Find the range in which the block can be kept without slipping when the block is pulled or pushed towards the spring (spring is elongated or compressed). Take g=10 m/s2.


A
3.2 m
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B
1.6 m
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C
2.4 m
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D
4.8 m
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Solution

The correct option is A 3.2 m
When the spring is compressed:
By say x1, from FBD we get (here, R is the normal force)

Where x1 is compression
x1=x0x0
To keep the block without slipping i.e., keeping it in equilibrium using
Fx=0
fs=kx1
and, Fy=0
R=2g
fs=μsR=0.8×2×10=16 N
x1=fsk=1610=1.6 m

When the spring is elongated:
By say x2, from FBD we get

Where x2 is elongation
x2=x′′0x0
At equilibrium,
Fx=0
kx2=fs
and, Fy=0
R=mg
fs=μsR=0.8×2g=16 N
x2=fsk=1610=1.6 m

Range in which block can be kept without slipping is
x1+x2=1.6+1.6=3.2 m

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