Question

A particle moves from a point r₁ = (2 m) i + (3 m) j to another point r₂ = (3 m) i + (2 m) j during which a certain force F=(5 N) i + (5 N) j acts on it. Find the work done by the force on the particle during the displacement.
Concept of Physics - 1 , HC VERMA , Chapter " Work and Energy"

Answer 1

Hello Dear.

Given conditions ::-

r₁ = (2m) i + (3m) j
r₂ = (3m) i + (2m) j
F = (5N) i + (5N) j

Hence the displacement of the particle r ,

r = r₂ - r₁

r = { (3m) i + (2m) j } - { (2m) i + (3m) j }
r = (1 m) i - (1m) j

For finding the work done(w) = Dot product of the given vector F & r .
w= F.r

as given F = (5N) i + (5N) j
Now,
w = { (5N) i + (5N) j } . { (1m) i - (1m) j }
w = [- (5N ) × 1m ] + [ (5N) × 1m ]
w = -5J +5J
w= 0 

Hence the work done by through the force on the particle during its displacement is 0 (Zero) .


Hope it Helps.

Answer 2

Answer:

Displacement = r2 - r1

⇒ Displacement = ( 3i + 2j ) m - ( 2i + 3j ) m

⇒ Displacement = ( 3i - 2i + 2j - 3j ) m

⇒ Displacement = ( i - j ) m

Given that Force = ( 5i + 5j ) N

Work Done = Force · Displacement

⇒ Work Done = ( 5i + 5j ) N . ( i - j ) m

⇒ Work Done = ( 5i . i + 5j . -j ) J

⇒ Work Done = 5 - 5 J

⇒ Work Done = 0 J

Hence there is no work done by the particle.

Hope it helped !!

Thanks !!