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Question

A small block of mass 200 g is pressed against a horizontal spring fixed at one end to compress the spring through 5 cm. The spring constant is 100 N/m. The spring is located on a frictionless horizontal plank located at a height of 3 m from the ground. When the block is released, what horizontal distance will it travel (after leaving the plank) before it hits the ground. (Take g=10 m/s2).


A
1 m
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B
0.90 m
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C
0.85 m
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D
1.2 m
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Solution

The correct option is C 0.85 m
Given :
m=200 g=0.2 kg,k=100 N/m,x=5 cm =0.05 m,g=10 m/s2

Taking horizontal plank as a reference.
Let the block hit the ground with velocity v.
From energy conservation :
Ui+Ki=Uf+Kf
12kx2=0+12mv2
v=100×(0.05)20.2=1.11 m/sec

Applying equation of motion in y direction
(Given : 3 m below spring ) and take downward +ve
3=ut+12gt2
3=12gt2t=6g=0.77 s

Displacement in x - direction
d=ux×t+12axt2
=uxt (as ax=0 in horizontal direction)
d=ux×t=1.11×0.77
d=0.85 m

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