Question

an object of mass 4 kg is whirled round a vertical circle radius 1m with a constant speed of 3 metre per second calculate the maximum tension in the string

Answer 1

Answer:

• $\boxed{\sf Maximum \ tension \ (T_{\tiny max}) = 76 \ N}$

Given :

• Mass (m) = 4 kg
• Constant speed (v) = 3 m/s
• Radius of vertical circle (r) = 1 m
• Accelration due gravity (g) = 10 m/s²

To Find :

• Maximum tension in the string $\sf (T_{\tiny max})$

Explanation:

• As the object is moving in a vertical circular path. So, the maximum tension on the string Tis when the body will be on its lowest position because at that point centrifugal force and force due to gravity both will act on the body in same direction. So, Maximum tension $(\sf T_{max} )$ is the string will be equal to centrifugal force $\sf (F_c)$ + Force due to gravity :]

$\boxed{\boxed{ \bold{ T_{max} = F_c + mg= \frac{m {v}^{2} }{r} + mg }}}$

Substituting value of m, v, r & g in the equation:

$:\implies \sf T_{\tiny max} = \dfrac{4 \times 3^2}{1} + 4 \times 10$

$:\implies \sf T_{\tiny max} = \dfrac{4 \times 9 }{1} + 40$

$:\implies \sf T_{\tiny max} = 36 + 40$

$:\implies \underline{ \boxed{ \sf T_{\tiny max} = 76 \: N }}$

Therefore, Maximum tension in the string (T) = 76 N.