A particle of mass M = 0 . 2   kg is initially at rest in the x y -plane at a point x = − l ,…

A particle of mass M=0.2 kg is initially at rest in the xy-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?
  1. The particle arrives at the point x=l, y=-h at time t=2 s.
  2. τ→=2k^ when the particle passes through the point x=l, y=-h.
  3. L→=4k^ when the particle passes through the point x=l, y=-h.
  4. τ→=k^ when the particle passes through the point x=0, y=-h.

Solution

At t=2 s:

displacement along +X axis

=12×10×t2

=12×10×4=20 m

Hence, particle arrives at 10,-1

At x=l, y=−h,

τ→=r→×F→

=10i^−j^×0.2×10i^=2k^ N m

L→=r→×p→=10i^−j^×0.2×vi^

and vat t=2s=0+10×2=20 m s-1

∴  L→=10i^−j^×4i^=4k^ N m s

At x=0,y=−h:

r→=0i^−j^

F→=2i^

∴  τ→=r→×F→=2k^ N m

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Asked in: JEE Advanced 2021 (Paper 1)

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