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Q.

Consider a body of mass 1.0 𝑘𝑔 at rest at the origin at time t=0. A force F→=αt i^+β j^ is applied on the body, where α=1.0N/s and β=1.0N . The torque acting on the body about the origin at time t=1.0s is τ→ . Which of the following statements is (are) true?

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a

τ→=13Nm

b

The torque τ→ is in the direction of the unit vector +k^

c

The velocity of the body at t=1s is v→=12i^+2j^m/s

d

The magnitude of displacement of the body at t=1s is 16m

answer is A.

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Detailed Solution

F→=(αt)i^+βj^⇒F→=ti^+j^,⇒mdv→dt=ti^+j^On Integrating⇒mv→=t22i^+tj^⇒dr→dt=t22i^+tj^On Integrating⇒r→=t36i^+t22j^ At t=1s,r→=(r→×F→)=16i^+12j^×(i^×j^)=−13k^At t=1s,v→=12i^+j^=12(i^+2j^)m/sec At t=1s,s→=r→1−r→0⇒s→=16i^+12j^⇒|s→|=162+122=106m

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Consider a body of mass 1.0 at rest at the origin at time t=0. A force F→=αt i^+β j^ is applied on the body, where α=1.0N/s and β=1.0N . The torque acting on the body about the origin at time t=1.0s is τ→ . Which of the following statements is (are) true?