Question

A particle is performing vertical circular motion. The difference in tension at lowest and highest point is

• A. $2mg$
• B. $6mg$
• C. $8mg$
• D. $4mg$

Hint:

In vertical circular motion, the difference in tension between lowest and highest point is always $6mg$ for a complete circle.

Answer 1

The Correct Option is B

Step 1: Tension at lowest point.
At the lowest point: \[ T_L = \dfrac{mv^2}{r} + mg \] Step 2: Tension at highest point.
At the highest point: \[ T_H = \dfrac{mv^2}{r} - mg \] Step 3: Difference in tension.
\[ T_L - T_H = \left(\dfrac{mv^2}{r} + mg\right) - \left(\dfrac{mv^2}{r} - mg\right) \] Step 4: Simplification.
\[ T_L - T_H = 2mg + 4mg = 6mg \]