Question

22. A block follows the path as shown in the figure from height h. If radius of circular path is t, then relation holds good to complete full circle is
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Answer 1

The relation holds good to complete full circle is h > 5t/2

For the block to complete a full circle, it should have a non zero, positive normal force when it is at the highest point of the path.

Let Velocity at point A  = Va

At A Force equation

• mg + N =  $\frac{mVa^{2} }{t}$

Let Velocity at B be Vb

At B applying energy conservation

• 0.5mVb^2  = 0.5mVa^2 + mg (2t)

As,

• $v_a^2 > gt$

• $\dfrac {mv_b^2}{2} > 2mgt +\dfrac {mgt}{2} \ \Rightarrow \ \dfrac {mv_b^2}{2} > \dfrac {5mgt}{2}$

Applying Energy conservation between points B and at height h,

• mVb^2 / 2  = mgh

Combining both conditions,

• mgh > 5mgt/2
• h > 5t/2