Work done when a force F -2 -3 k- N acting on a particle displaces it from the point r 1-k- to the point r 2-2 k- isA- 7 JB- -1 JC- 1 JD- -3 J

Given constant force F=î+2ĵ+3k̂ N Initial position r_1=(î+ĵ+k̂) m Final position r_2=(î ĵ+2k̂) m Work done (W)=F.s To find the displacement s: s=r_2 r_1= chan ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Work Done as Dot Product

Work done whe...

Question

Work done when a force $\to F = (^i + 2^j + 3^k) N$ acting on a particle displaces it from the point $r_{1} = (^i +^j +^k)$ to the point $r_{2} = (^i -^j + 2^k)$ is

- 3 J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7 J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 1 J

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $- 1 J$
Given constant force $\to F =^i + 2^j + 3^k N$
Initial position $_{1} = (^i +^j +^k) m$
Final position $_{2} = (^i -^j + 2^k) m$
Work done $(W) = \to F . \to s$

To find the displacement $\to s$ :
$\to s =_{2} -_{1} =$ change in position
$\to s = (^i -^j + 2^k) - (^i +^j +^k)$
$\to s = (- 2^j +^k) m$

We know that, if $\to A = A_{x}^i + A_{y}^j + A_{z}^k; \to B = B_{x}^i + B_{y}^j + B_{z}^k$ ,
then $\to A . \to B = A_{x} B_{x} + A_{y} B_{y} + A_{z} B_{z}$

$∴ W = \to F . \to s = (^i + 2^j + 3^k) . (- 2^j +^k)$
$W = 1 (0) + 2 (- 2) + 3 (1)$
$W = - 4 + 3 = - 1$
$∴$ Workdone $(W) = \to F . \to s = - 1 J$

Hence option C is the correct answer.

Suggest Corrections

Similar questions

Q. Work done when a force

\to F = (^i + 2^j + 3^k) N

acting on a particle displaces it from the point

r_{1} = (^i +^j +^k)

to the point

r_{2} = (^i -^j + 2^k)

Q. Work done when a force

\to F = (^i + 2^j + 3^k) N

acting on a particle takes it from the point

_{1} = (^i +^j +^k)

to the point

_{2} = (^i -^j + 2^k)

Q. Work done by a force

F = (^i + 2^j + 3^k) N

acting on a particle in displacing it from the point

_{1} =^i +^j +^k

to the point

_{2} =^i -^j + 2^k

Q. Work done by a force

\to F = (^i + 2^j + 3^k) N

action on a particle in displacing it from the point

{\to r}_{1} =^i +^j +^k

to the point

{\to r}_{1} =^i -^j - 2^k

Q. A force

\to F =^i + 3^j + 2^k

acts on a particle to displace it from the point

(^i + 2^j - 3^k)

to the point

B (3^i -^j + 5^k) .

The work done by the force will be

Join BYJU'S Learning Program

Work done when a force →F=(^i+2^j+3^k) N acting on a particle displaces it from the point r1=(^i+^j+^k) to the point r2=(^i−^j+2^k) is

Work done when a force $\to F = (^i + 2^j + 3^k) N$ acting on a particle displaces it from the point $r_{1} = (^i +^j +^k)$ to the point $r_{2} = (^i -^j + 2^k)$ is