JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Work, Power & Energy

A force

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.

(A)0
(B) $\frac{1}{2}$ ✓ Correct
(C) $\frac{1}{3}$
(D)2

Answer: (B)

Solution

Work done is

W = F \cdot S

, with

F = 2 \hat{i} + b \hat{j} + \hat{k}

and

S = \hat{i} - 2 \hat{j} - \hat{k}

W = (2) (1) + (b) (- 2) + (1) (- 1) = 2 - 2 b - 1 = 1 - 2 b

Setting W = 0:

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

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Single correct option

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