JEE Advanced2016PhysicsMotion in One DimensionActual
The positon vector r → of a particle of mass m is given by the following equation r → t = α t 3 i ^ + β t 2 j ^ , w h e r e α = 10 3 m s - 3 , β = 5 m s - 2 a n d m = 0.1 k g . A t t = 1 s , which of the following statements (s) is (are) true about the particle?
Options
- AThe velocity v → is given by v → = 10 i ^ + 10 j ^ m s - 1
- BThe angular momentum L → with respect to the origin is given by L → = - 5 3 k ^ N m s
- CThe force F → is given by F → = i ^ + 2 j ^ N
- DThe torque τ → with respect to the origin is given by τ → = - 20 3 k ^ N m
Correct answer
A. The velocity v → is given by v → = 10 i ^ + 10 j ^ m s - 1
Step-by-step solution
r → = α t 3 i ^ + β t 2 j ^ v → = d r → d t = 3 α t 2 i ^ + 2 β t j ^ a → = d 2 r → d t 2 = 6 α t i ^ + 2 β j ^ At t = 1 (i) v → = 3 × 10 3 × 1 i ^ + 2 × J × 1 j ^ = 10 i ^ + 10 j ^ (ii) L → = r → × p → = 10 3 × 1 i ^ + 5 × 1 j ^ × 0.1 10 i ^ + 10 j ^ = - 5 3 k ^ (iii) F → = m × 6 × 10 3 × 1 i ^ + 2 × 5 j ^ = 2 i ^ + j ^ (iv) τ → = r × F → = 10 3 i ^ + 5 j ^ × 2 i ^ + j ^ = + 10 3 k ^ + 10 - k ^ = - 20 3 k ^