At t=0 , a body of mass 100 g starts moving under the influence of a force (5 i +10 j ) N. After 2 s its position is (2x i +5y j ) m. The ratio x:y is ______.

Step-by-step solution

Mass m = 100 g = 0.1 kg Force F = 5 i + 10 j N Acceleration a = F m = 5 i + 10 j 0.1 = 50 i + 100 j m/s ^2 Since the body starts from rest, initial velocity u = 0 . Position after t = 2 s is given by r = u t + 1 2 a t^2 r = 1 2 (50 i + 100 j )(2)^2 = 100 i + 200 j m Comparing with the given position r = 2x i + 5y j : 2x = 100 x = 50 5y = 200 y = 40 The ratio x:y = 50:40 = 5:4 Answer: 5:4