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Q.

A force $\vec{F} = 2 \hat{i} + b \hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i} - 2 \hat{j} - \hat{k} .$ What will be the value of b, if work done on the particle is zero.

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a

$0$

b

$2$

c

$\frac{1}{2}$

d

$\frac{1}{3}$

answer is B.

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Detailed Solution

The dot product of $\vec{F}$ and $\vec{d}$ is:

$\vec{F} \cdot \vec{d} = (2) (1) + (b) (- 2) + (1) (- 1) = 1 - 2 b$

Set $\vec{F} \cdot \vec{d} = 0$ (since the work done is zero):

$1 - 2b = 0$

$b = \frac{1}{2}$

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A force F→=2i^+bj^+k^ is applied on a particle and it undergoes a displacement i^−2j^−k^. What will be the value of b, if work done on the particle is zero.