A uniform force of (2i + j ) + N acts on a particle of mass 1 kg. The particle displaces from position m to m.

Question

A uniform force of (\(2\hat i + \hat j\)) + N acts on a particle of mass 1 kg. The particle displaces from position(\(3 \hat j +\hat k\)) m to (\(5\hat i + 3\hat j\)) m. Th e work done by the force on the particle is

(a) 9 J 

(b) 6 J 

(c) 10 J 

(d) 12 J

Answer 1

Correct answer is (c) 10 J

Given,

Force, F = \(2 \hat i + \hat j\)

\(\vec r_1\) = (\(3 \hat j + \hat k\)) m

\(\vec r_2\) = (\(5 \hat i + 3\hat j\)) m

Therefore,

\(\vec S\) = \(\vec r_2\) - \(\vec r_1\)

=  (\(5 \hat i + 3\hat j\)) -  (\(3 \hat j + \hat k\))

= \(5 \hat i + 3\hat j\) - \(3 \hat j - \hat k\)

= ( \(5 \hat i - \hat k\)) m

Therefore,

\(W = \vec F.\vec S\)

= (\(2 \hat i + \hat j\)).( \(5 \hat i - \hat k\))

= 10 J

Comments

Pls can u show your workings that would be helpful