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 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
Updated On: Jul 5, 2022
- 100 J
- 50 J
- 200 J
- 75 J
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The Correct Option is A
Solution and Explanation
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$
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration