The position of an object having mass 0.1 kg as a function of time t is given as r = (10t^2 i + 5t^3 j ) m. At t = 1 s, which of the following statements are correct ? A. The linear momentum p = (2 i + 1.5 j ) kg·m/s. B. The force acting on the object F = (2 i + 3 j ) N. C. The angular momentum of the object about its origin L = 15 k J·s. D. The torque acting on the object about its origin = 20 k N·m. Choose the corr

Step-by-step solution

Given the position vector r = 10t^2 i + 5t^3 j Velocity v = d r dt = 20t i + 15t^2 j Acceleration a = d v dt = 20 i + 30t j At t = 1 s: r = 10 i + 5 j m v = 20 i + 15 j m/s a = 20 i + 30 j m/s ^2 Linear momentum p = m v = 0.1(20 i + 15 j ) = 2 i + 1.5 j kg m/s (Statement A is correct) Force F = m a = 0.1(20 i + 30 j ) = 2 i + 3 j N (Statement B is correct) Angular momentum L = r p = (10 i + 5 j ) (2 i + 1.5 j ) = (10 1.5 - 5 2) k = 5 k J s (Statement C is incorrect) Torque = r F = (10 i + 5 j ) (2 i + 3 j ) = (10 3