At t = 0, a body of mass 100 g starts from rest under the action of a constant force F = (5î+10ĵ) N. After 2 s, its position vector is r = (2x î+5y ĵ) m. What is the ratio x:y?
Options

Question

At t = 0, a body of mass 100 g starts from rest under the action of a constant force F = (5î+10ĵ) N. After 2 s, its position vector is r = (2x î+5y ĵ) m. What is the ratio x:y?

G1 Physics · Accepted Answer

The mass is m = 100 g = 0.1 kg. Therefore the acceleration is a = F ÷ m = (5î+10ĵ) ÷ 0.1 = 50î+100ĵ m·s⁻². The body starts from rest, so r = (1 ÷ 2)at². At t = 2 s: r = (1 ÷ 2)(50î+100ĵ)(2)² = 100î+200ĵ m. But the position is also given as r = 2x î+5y ĵ. Comparing components: 2x = 100 ⇒ x = 50, 5y = 200 ⇒ y = 40. Hence, x:y = 50:40 = 5:4. Correct option: D.