A uniform force of (3 hati + hatj) newton acts on a particle of mass 2kg. Hence the particle is displaced from position (2 hati + hatk ) meter to position (4 hati + 3 hatj - hatk) meter. The work done by the force on the particle is :

Question

A uniform force of (3 hati + hatj) newton acts on a particle of mass 2kg. Hence the particle is displaced from position (2 hati + hatk ) meter to position (4 hati + 3 hatj - hatk) meter. The work done by the force on the particle is : (A) 15 J (B) 9 J (C) 6 J (D) 13 J

Tardigrade Admin · Accepted Answer

W = vecF. vecS = (3 hati + hatj) .[(4 -2) hati + (3 - 0) hatj + ( - 1 - 1) hatk] = (3 hati + hatj) .(2 hati + 3 hatj - 2 hatk) = 3(2) + 1(3) + 0( - 2) = 9 J

Q. A uniform force of $(3 \hat{i} + \hat{j})$ newton acts on a particle of mass 2kg. Hence the particle is displaced from position $(2 \hat{i} + \hat{k})$ meter to position $(4 \hat{i} + 3 \hat{j} - \hat{k})$ meter. The work done by the force on the particle is :

15 J

9 J

6 J

13 J

$W = F . S = (3 \hat{i} + \hat{j}) . [(4 - 2) \hat{i} + (3 - 0) \hat{j} + (- 1 - 1) \hat{k}]$
$= (3 \hat{i} + \hat{j}) . (2 \hat{i} + 3 \hat{j} - 2 \hat{k})$
$= 3 (2) + 1 (3) + 0 (- 2) = 9 J$

Q. A uniform force of (3i^+j^​) newton acts on a particle of mass 2kg. Hence the particle is displaced from position(2i^+k^) meter to position (4i^+3j^​−k^) meter. The work done by the force on the particle is :

15 J

9 J

6 J

13 J

W=F.S=(3i^+j^​).[(4−2)i^+(3−0)j^​+(−1−1)k^] =(3i^+j^​).(2i^+3j^​−2k^) =3(2)+1(3)+0(−2)=9J

Q. A uniform force of $(3 \hat{i} + \hat{j})$ newton acts on a particle of mass 2kg. Hence the particle is displaced from position $(2 \hat{i} + \hat{k})$ meter to position $(4 \hat{i} + 3 \hat{j} - \hat{k})$ meter. The work done by the force on the particle is :

$W = F . S = (3 \hat{i} + \hat{j}) . [(4 - 2) \hat{i} + (3 - 0) \hat{j} + (- 1 - 1) \hat{k}]$
$= (3 \hat{i} + \hat{j}) . (2 \hat{i} + 3 \hat{j} - 2 \hat{k})$
$= 3 (2) + 1 (3) + 0 (- 2) = 9 J$