Work, KE/PE, mechanical energy, power, units MCQs

Q1. A ball is thrown vertically up with velocity 20 m/s. At what height does its KE become equal to half its initial KE (g = 10 m/s²)?

• A.10 m
• B.5 m
• C.20 m
• D.15 m

Answer: A. 10 m

Spot-the-setup - a typical physics numerical. The data on the table: 20 m, 10 m. We are after the quantity the stem asks for. Tool of choice - Initial KE = ½mv² = 200m/2 = m·200/2 - using m = 1 kg: KE_i = 200 J. Rearrange it for the unknown before substituting. Numbers in: Initial KE = ½mv² = 200m/2 = m·200/2 - using m = 1 kg: KE_i = 200 J → At height h, PE = 10h, KE = 200 − 10h = 100 ⇒ h = 10 m. Lock in option A) 10 m.

Q2. A body is dropped from a height of 20 m. At what height above the ground does it possess equal amounts of kinetic and potential energy (assuming PE = 0 at ground)?

• A.10 m
• B.5 m
• C.15 m
• D.8 m

Answer: A. 10 m

Given 20 m, asked for the unknown. By Total mechanical energy = mg(20). Total mechanical energy = mg(20) → For KE = PE = ½ of total, PE = mg·h = mg·10, so h = 10 m. Thus option A) 10 m.

Q3. Dragging a sack of grain across a yard, a labourer applies 8 N and shifts it 12 m along the same line. What work is performed?

• A.96 J
• B.20 J
• C.0.6667 J
• D.48 J

Answer: A. 96 J

Force and displacement are along the same line, so W = F*d = 8 N * 12 m = 96 J.