Grade 12Mechanics

A block A slides down a smooth inclined plane when released from the top in time t. Another block falls freely from the same point and strikes the ground in time t/2. The value of angle teta is

mrli

8 Years agoGrade 12

1 Answer

Arun

8 Years ago

Dear Student

If angle of inclination is θ, then the acceleration with which the block slides on the incline is g sin $\theta$ .

Given that the block is taking a time t/2 and when it is left freely falling from the same height, then the block falls with an acceleration g, at this time it is taking a time t. therefore

S = u* t + (1/2)*g *t^2

h = 0 – (1/2)*g sin $\theta$ * t^2

t^2 = 2 h/ g sin $\theta$

and

h sin $\theta$ = (1/2)*g *(t/2)^2

t^2 = 8 h sin $\theta$ / g

Now

8 h sin $\theta$ / g = 2 h/ g sin $\theta$

sin² $\theta$ = ¼

sin $\theta$ = ½

$\theta$ = 30 degree

Regards

Arun (askIITians forum expert)

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A block A slides down a smooth inclined plane when released from the top in time t. Another block falls freely from the same point and strikes the ground in time t/2. The value of angle teta is

mrli

1 Answer

Arun

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