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Question

The velocity-time graph in the figure given below shows the motion of a wooden block of mass 1 kg which is given an initial push at t=0 along a horizontal table. Which of the following statements is/are correct ?


A
The coefficient of friction between the block and the table is 0.1
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B
The coefficient of friction between the block and the table is 0.2
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C
If the table has half of its present roughness, the time taken by the block to complete the journey is 4 s
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D
If the table has half of its present roughness, the time taken by the block to complete the journey is 8 s
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Solution

The correct options are
A The coefficient of friction between the block and the table is 0.1
D If the table has half of its present roughness, the time taken by the block to complete the journey is 8 s
From the vt graph:
dvdt=Slope=(04)(40)=1
a=dvdt=1 m/s2

Negative acceleration is a result of friction acting on the block in opposite direction.
f=m|a|=1×1=1 N in opposite direction to the motion

f=μN=μmg
μ=110=0.1

If surface roughness becomes half; μ=0.05
f=0.05×10=0.5 N
and |a|=0.51=0.5 m/s2

For block to complete its journey: (Final velcoity is zero)
u=4 m/s, v=0,a=0.5 m/s2
From v=u+at
0=4(0.5)t
t=8 s

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