A body moves from a position r1=(2 hati - 3 hatj - 4 hatk) m to a position, r2=(.3 hati-4 hatj+5 hatk.) m under the influence of a constant force F=(4 hati + hatj + 6 hatk) N . The work done by the force is

Question

A body moves from a position r1=(2 hati - 3 hatj - 4 hatk) m to a position, r2=(.3 hati-4 hatj+5 hatk.) m under the influence of a constant force F=(4 hati + hatj + 6 hatk) N . The work done by the force is (A) 57 J (B) 58 J (C) 59 J (D) 60 J

Tardigrade Admin · Accepted Answer

Given, r1=2 hati-3 hatj-4 hatk And r2=3 hati-4 hatj+5 hatk Now, r2-r1= hati- hatj+9 hatk And F=4 hati+ hatj+6 hatk ∴ work done = F.r W=(4 hati + hatj + 6 hatk).(. hati- hatj+9 hatk ) =4-1+54=57 J

Q. A body moves from a position r1​=(2i^−3j^​−4k^)m to a position, r2​=(3i^−4j^​+5k^)m under the influence of a constant force F=(4i^+j^​+6k^)N . The work done by the force is

57 J

58 J

59 J

60 J

Given, r1​=2i^−3j^​−4k^ And r2​=3i^−4j^​+5k^ Now, r2​−r1​=i^−j^​+9k^ And F=4i^+j^​+6k^ ∴ work done = F.r W=(4i^+j^​+6k^).(i^−j^​+9k^ ) =4−1+54=57J

Q. A body moves from a position $r_{1} = (2 \hat{i} - 3 \hat{j} - 4 \hat{k}) m$ to a position, $r_{2} = (3 \hat{i} - 4 \hat{j} + 5 \hat{k}) m$ under the influence of a constant force $F = (4 \hat{i} + \hat{j} + 6 \hat{k}) N$ . The work done by the force is