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Consider a body of mass 1.0 at rest at ...

Consider a body of mass 1.0 at rest at the origin at time `t = 0`. A force `vec F=(alpha t hat l +beta hat J) ` is applied on the body, where `alpha =1.0 Ns^(-1) and beta =1.0 N`. The torque acting on the body about the origin at time `t=1.0 s " is " vec tau` . Which of the following statements is (are) true?

A

|vectau|=1/3 Nm`

B

`The torque `vectau` is in the direction of the unit vector `-hatk`

C

The velocity of the body at `t=1s` is `vecv =1/2 (hati + 2hatj)ms^(-1)`

D

The magnitude of displacement of the body at t=1s is `1/6` m

Text Solution

Verified by Experts

The correct Answer is:
A, C
`veca = thati + hatj m//s^(2)`
`rArr vecv = t^(2)/2 hati + thatj m//s rArr vecr =t^(3)/6 hati + t^(2)/2 hatj m`
So, `vectau = vecr xx vecF =(t^(3)/2 - t^(3)/6) (-hatk) = t^(3)/3 (-hatk) Nm`
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