Question

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 √7gr at the lowest point. The tension in the string at the lowest point is ?​

Answer 1

Solution:

As per the given data,

• The velocity of the point mass at the lowest point =√7gr

$\blacksquare \:$ At the lowest point:

Three forces are acting on the point mass

• Gravitational force (mg) in the downward direction.
• Centripetal force (mv²/r ) in the downward direction.
• Tension is acting in an upward direction.

Net force,

⇒ T = mg + mv²/r

⇒ T = mg + m (√7gr)²/r

⇒ T = mg + m x 7gr / r

⇒ T = mg + 7 mg

⇒ T = 8 mg

The tension in the string at the lowest point is 8mg.

Answer 2

Answer:

8mg

Explanation:

tension at lowest point

T=mg+mv^2/I

here I is R

T=mg+mv^2/r

T=mg+m(√7gr)^2/r

T=mg+m(7gr)/r

T=mg+7mg

T=8mg