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NEET PHYSICSEasy

A point mass $m$ is moved in a vertical circle of radius $r$ with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is:

A

$6mg$

B

$7mg$

C

$8mg$

D

$mg$

Step-by-Step Solution

Identify Forces: At the lowest point of the vertical circle, the forces acting on the mass are:

Tension ( $T$ ) acting vertically upwards (towards the center).
Weight ( $mg$ ) acting vertically downwards.

Apply Newton's Second Law: The net force towards the center provides the centripetal force ( $F_c$ ) required for circular motion. $T - mg = \frac{mv^2}{r}$ [Source 128]
Substitute Given Values:

Velocity at the lowest point, $v = \sqrt{7gr}$ .
Radius $= r$ . $T - mg = \frac{m(\sqrt{7gr})^2}{r}$ $T - mg = \frac{m(7gr)}{r}$ $T - mg = 7mg$

Solve for Tension: $T = 7mg + mg = 8mg$ [Source 50]

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