Question

A ball is held at rest at position A by two light strings. The horizontal string is cut and the ball starts swinging as a pendulum point B is the farthest to the right the ball goes as it swings back and forth. What is the ratio of the tension in the supporting string in position B to its value at A before the horizontal string was cut.

• A. sin²b
• B. cos²b
• C. tan²b
• D. cosb

Answer 1

Answer: (B)

cos²b

Answer 2

At : A

T¢cosb

T¢cosb = mg

T¢ = $\frac{mg}{\cos\beta}$

At : B

T¢¢ – mg cos b = $\frac{mv^{2}}{1}$

at B ; v = 0

T¢¢ = mg cos b

$\frac{T''}{T'}$ = $\frac{mg\cos\beta}{mg/\cos\beta}$

$\frac{TensionatB}{TensionatA}$ = $\frac{\mathbf{T}''}{\mathbf{T}'} = \mathbf{co}\mathbf{s}^{\mathbf{2}}\mathbf{\beta}$