A force is applied on a particle and it undergoes a displacement . What will be the value b, if work done on the particle is zero. [2025]

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Solution

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. [2025]

1 0

2 $\frac{1}{2}$

3 $\frac{1}{3}$

4 2

Ans.
(2)

Given, W = 0

$∴ \vec{F} \cdot \vec{S} = 0$

$(2 \hat{i} + b \hat{j} + \hat{k}) \cdot (\hat{i} - 2 \hat{j} - \hat{k}) = 0$

$2 - 2 b - 1 = 0 \Rightarrow b = \frac{1}{2}$

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