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Rotational Motion question

2016 · Shift 1 · Q40
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Rotational Motion question

2016 · Shift 1 · Q40

JEE AdvancedPhysicsRotational MotionMultiple correct+4 / −2
The position vector r→\overrightarrow rr of a particle of mass m is given by the following equation r→(t)=αt3i^+βt2j^,\overrightarrow r \left( t \right) = \alpha {t^3}\widehat i + \beta {t^2}\widehat j,r(t)=αt3i+βt2j​, where α=103ms−3\alpha = {{10} \over 3}m{s^{ - 3}}α=310​ms−3, β=5 ms−2\beta = 5\,m{s^{ - 2}}β=5ms−2 and m = 0.1 kg. At t = 1 s, which of the following statement(s) is(are) true about the particle?
  1. A
    The velocity v→\overrightarrow vv is given by v→=(10i^+10j^)\overrightarrow v = \left( {10\widehat i + 10\widehat j} \right)v=(10i+10j​) ms-1
  2. B
    The angular momentum L→\overrightarrow LL with respect to the origin is given by L→=−(53)k^ N m s\overrightarrow L = - \left( {{5 \over 3}} \right)\widehat k\,N\,m\,sL=−(35​)kNms
  3. C
    The force F→\overrightarrow FF is given by F→=(i^+2j^)N\overrightarrow F = \left( {\widehat i + 2\widehat j} \right)NF=(i+2j​)N
  4. D
    The torque τ→\overrightarrow \tauτ with respect to the origin is given by τ→=−(203)k^ N m\overrightarrow \tau = - \left( {{{20} \over 3}} \right)\widehat k\,N\,mτ=−(320​)kNm
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