Question

A particle moves from position $r_1 = 3 \hat i + 2 \hat j - 6 \hat k$ to position $r_2 = 14 \hat i + 13 \hat j + 9 \hat k$ under action of force $F = 4 \hat i + \hat j + 3 \hat k$ N. The work done will be

• A. 100 J
• B. 50 J
• C. 200 J
• D. 75 J

Answer 1

Answer: (A)

100 J

Answer 2

Using the formula for work done $W = F . r = F . (r_2 - r_1)$ $W = (4 \hat i + \hat j + 3 \hat k) . (14 \hat i + 13 \hat j + 9 \hat k - 3 \hat i - 2 \hat j + 6 \hat k)$ $\Rightarrow W = (4 \hat i + \hat j + 3 \hat k) . (11 \hat i + 11 \hat j + 15 \hat k)$ or $W = 44 + 11 + 45 = 100 \, J$