A particle of mass M = 0 . 2 kg is initially at rest in the x y -plane at a point x = − l , y = − h , where l = 10 m and h = 1 m . The particle is accelerated at time t = 0 with a constant acceleratio

Question

A particle of mass M = 0 . 2 kg is initially at rest in the x y -plane at a point x = − l , y = − h , where l = 10 m and h = 1 m . The particle is accelerated at time t = 0 with a constant acceleration a = 10 m s - 2 along the positive x -direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by L → and τ → , respectively. i ^ , j ^ and k ^ are unit vectors along the positive x , y and z -directions, respectively. If k ^ = i ^ × j ^ then which of the following statement(s) is (are) correct?

TestHub · Accepted Answer

At t = 2 s : displacement along + X axis = 1 2 × 10 × t 2 = 1 2 × 10 × 4 = 20 m Hence, particle arrives at 10 , - 1 At x = l , y = − h , τ → = r → × F → = 10 i ^ − j ^ × 0 .2 × 10 i ^ = 2 k ^ N m L → = r → × p → = 10 i ^ − j ^ × 0 .2 × v i ^ and v at t = 2 s = 0 + 10 × 2 = 20 m s - 1 ∴ L → = 10 i ^ − j ^ × 4 i ^ = 4 k ^ N m s At x = 0 , y = − h : r → = 0 i ^ − j ^ F → = 2 i ^ ∴ τ → = r → × F → = 2 k ^ N m

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