An object of mass 0.1 kg has position vector r = 10t²î+5t³ĵ metres. At t = 1 s, consider the following statements:
A. Its linear momentum is p = (2î+1.5ĵ) kg·m·s⁻¹.
B. The force acting on it is F = (2î+3ĵ) N.
C. Its angular momentum about the origin is L = 15k̂ J·s.
D. The torque about the origin is τ = 20k̂ N·m.
Which statements are correct?

Question

An object of mass 0.1 kg has position vector r = 10t²î+5t³ĵ metres. At t = 1 s, consider the following statements:

A. Its linear momentum is p = (2î+1.5ĵ) kg·m·s⁻¹.
B. The force acting on it is F = (2î+3ĵ) N.
C. Its angular momentum about the origin is L = 15k̂ J·s.
D. The torque about the origin is τ = 20k̂ N·m.

Which statements are correct?

G1 Physics · Accepted Answer

Given, r = 10t²î+5t³ĵ. Velocity: v = dr ÷ dt = 20tî+15t²ĵ. At t = 1 s, v = 20î+15ĵ m·s⁻¹. Therefore momentum is p = mv = 0.1(20î+15ĵ) = 2î+1.5ĵ kg·m·s⁻¹. So statement A is correct. Acceleration: a = dv ÷ dt = 20î+30tĵ. At t = 1 s, a = 20î+30ĵ m·s⁻². Therefore, F = ma = 0.1(20î+30ĵ) = 2î+3ĵ N. So statement B is correct. At t = 1 s, r = 10î+5ĵ m. Angular momentum: L = r×p. Its k-component is L(z) = (10)(1.5)-(5)(2) = 15-10 = 5. Hence, L = 5k̂ J·s. Therefore statement C is false. Torque: τ = r×F.…