Question

A body of mass 2kg is moving in a vertical of radius 2 metres .The work done when it moves from the lowest point to the highest point-
(a) 80 j
(b) 40 j
(c) 20 j
(d) 0

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\large\red{\boxed{\sf Work(W)=80J }}$

$\huge\underline\blue{\sf Solution:}$

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

• Mass (m) = 2kg

• Radius (r) = 2m

• Velocity at lowest point ($\sf{u_{lowest})=\sqrt{5gR}}$

• Velocity at highest point($\sf{v_{highest})=\sqrt{gR}}$

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

• Work done when it moves from the lowest point to the highest point (W)=?

━━━━━━━━━━━━━━━━━━━━━━━━━

According to Work-Energy Theorem :

$\large{♡}$$\large{\boxed{\sf W=Change\:in\:Kinetic\:Energy }}$

$\large\implies{\sf {\frac{1}{2}}mu^{2}-{\frac{1}{2}}mv^{2} }$

$\large\implies{\sf {\frac{1}{2}}m×5gR-{\frac{1}{2}}m×gR}$

$\large\implies{\sf {\frac{1}{2}}mgR(5-1) }$

$\large\implies{\sf {\frac{1}{2}}×2×10×2×4}$

$\large\implies{\sf W=80J }$

$\huge\red{♡}$$\large\red{\boxed{\sf Work(W)=80J }}$