Question

A body, constrained to move in y-direction, is subjected to a force given by $\overrightarrow{F} = (-2\widehat{i}+15\widehat{j}+6\widehat{k})$N The work done by this force in moving the body through a distance of 10$\widehat{j}$ m along y-axis, is

• A. 150 J
• B. 20 J
• C. 190 J
• D. 160 J

Answer 1

The Correct Option is A

To solve this problem, we need to understand how the work done by a force is calculated. The work done (W) by a force (\overrightarrow{F}) when moving an object through a displacement (\overrightarrow{d}) is given by the formula:

W = \overrightarrow{F} \cdot \overrightarrow{d}

where \cdot denotes the dot product.

Here, the force vector is given as \overrightarrow{F} = (-2\widehat{i} + 15\widehat{j} + 6\widehat{k}) N, and the displacement vector along the y-axis is \overrightarrow{d} = 10\widehat{j} m.

When calculating the dot product, we consider only the components of the vectors in the same direction. Thus:

• The \widehat{i} and \widehat{k} components do not contribute to work because their displacement components are zero.
• Only the \widehat{j} component is relevant.

The dot product here is:

W = (0 \cdot (-2)) + (15 \cdot 10) + (0 \cdot 6)

W = 0 + 150 + 0

W = 150 \, J

Thus, the work done by the force in moving the body through a distance of 10 meters along the y-axis is 150 J. Therefore, the correct answer is 150 J.