Question

A mass of 5 kg is moving along a circular path of radius Im. If the mass moves with 300 revolutions per minute, its kinetic energy would be​

Answer 1

$\large{\frak{Given}}\begin{cases}\sf{radius (R)= 1\:m}\\ \ \sf{mass(m)=5\:kg}\\ \ \sf{frequency(f)=300\:revmin^{-1}}\end{cases}$

$\large\underline{\frak{To\:Find:-}}$

• $\large{\textsf{Kinetic Energy of the object}}$

$\large\underline{\frak{solution:-}}$

★$\large{\textsf{ Angular velocity will be} }$

$\large\longrightarrow{\sf{2\pi f}}$

$\large\longrightarrow{\sf{300\times2\pi\:radmin^{-1}}}$

$\large\longrightarrow{\sf{300\times2\times3.14\:rad60^{-1}}}$

$\large\longrightarrow{\sf{\frac{\cancel{300}\times 2\times 3.14}{\cancel{60}}}}$

$\large\longrightarrow{\sf{10\pi\:rad}}$

$\large{\textsf{Relation between linear velocity }}$$\large{\textsf{and angular velocity is }}$

$\longrightarrow\sf{v= \omega R}$

$\large\longrightarrow{\sf{\frac{300\times2\pi}{60}\times1\:m}}$

$\large\longrightarrow{\sf{10\pi\:ms^{-1}}}$

★ $\large{\textsf{Now kinetic energy:-}}$

→ 1/2mv²

→ 1/2×5×(10π)²

→ 100π²×5×1/2

→ 250π² J