Question 43: Work, Energy and Power & Circular Motion

Question

A force $\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}$ 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.

Accepted Answer

To determine the value of $$b$$ such that the work done on the particle is zero, follow these steps:
The work done by a force on a displacement is given by the dot product:
$$	ext{Work} = \overrightarrow{F} \cdot \overrightarrow{d}.$$
Given the force
$$\overrightarrow{F} = 2\hat{i} + b\hat{j} + \hat{k},$$
and the displacement
$$\overrightarrow{d} = \hat{i} - 2\hat{j} - \hat{k},$$
compute the dot product:
$$\overrightarrow{F} \cdot \overrightarrow{d} = (2)(1) + (b)(-2) + (1)(-1).$$
Simplify the expression:
$$\overrightarrow{F} \cdot \overrightarrow{d} = 2 - 2b - 1 = 1 - 2b.$$
Since the work done is zero:
$$1 - 2b = 0.$$
Solve for $$b$$:
$$2b = 1,$$
$$b = \frac{1}{2}.$$
Thus, the value of $$b$$ is $$\frac{1}{2}$$, which corresponds to Option B.

Answer

$\frac{1}{3}$

Answer

$\frac{1}{2}$

Answer

0

Answer

2

Work, Energy and Power & Circular Motion

A force \overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{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.

Choose the correct answer: