Question

A body of mass 0.4 kg is whirled in a vertical
circle making 2 rev/sec. If the radius of the circle
is 1.2 m, then tension in the string when the body
is at the top of the circle, is
(a) 41.56 N (b) 89.86 N
(c) 109.86 N (d) 115.86 N

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec. If the radius of the circle

is 1.2 m, then tension in the string when the body

is at the top of the circle, is

$\huge\underline{\underline{\bf \orange{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• Mass of body (m) = 0.4kg
• Revolution/second = 2rev/s
• Radius (R)=1.2

$\large\underline{\underline{\sf To\:Find:}}$

• Tension at the top of circle (T)

❏$\large{\boxed{\bf \blue{T+mg=\dfrac{mv^2}{R}} }}$

$\implies{\sf T=\dfrac{mv^2}{R}-mg}$

$\implies{\sf \pink{v=\omega r}}$

⛬

$\implies{\sf T=m\omega^2r-mg }$

$\implies{\sf T=m[(\omega)^2-g ]}$

$\implies{\sf \omega = 2×2π }$

$\implies{\sf \pink{\omega =4π}}$

$\implies{\sf T=0.4[(4π)^2×1.2-10]}$

$\implies{\sf T=0.4[16π^2×1.2-10]}$

$\implies{\sf T= 0.4[189.3-10] }$

$\implies{\sf T=0.4×179.3}$

$\implies{\bf \red{Tension(T)=71.7N }}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Tension in the string when the body

is at the top of the circle, is ${\bf \red{71.7N}}$.