Question

When force (3, 2, 1) N acts on a body,
displacement of the body in the direction of Y-axis
is 50 cm calculate the work done.
A I J
B 1.5 J
C 4 J
D 3 J​

Answer 1

Answer:

• Option (A): 1 J

Given Information:

• Force = ( 3,2,1 ) N
• Displacement = 50 cm = 0.5 m, in the direction of y-axis.

To Find:

• Work Done by the body

We know that,

$\boxed{Work\:\:Done = Force \times Displacement}}$

Since Force is given in terms of coordinates, we first need to convert them into vector form. Converting coordinates of x to i, y to j and z to k, we get:

$\implies F = 3i + 2j + z$

Similarly Displacement is in y-axis. Hence we get:

$\implies Displacement = 0.5 j$

Taking the dot product of Force and Displacement we get:

$\implies F.s = 3i.(0.5j) + 2j.(0.5j) + 1k.(0.5j)\\\\\\\implies F.s = 1.5 i.j + 1 j.j + 0.5 j.k$

We know that, in dot product:

• i.j = j.k = k.i = 0
• i.i = j.j = k.k = 1

Hence applying it above, we get:

⇒ F.s = 1 N.m

We know 1 N.m = 1 J

Hence the Work done by the body is equal to 1 J.

Hence Option (A) is the correct answer.

Answer 2

$\Large\bf{\color{cyan}GiVeN,}$

• (3 , 2 , 1) N force acts on a body.

✒ If i , j & k are the unit vectors along x , y & z axes respectively, then

$\longmapsto\:\:\bf\blue{\vec{F}\:=\:3\hat{i}\:+\:2\hat{j}\:+\:1\hat{k}\:}$

• Displacement of body in direction of y-axis is 50 cm, i.e. 0.5 m.

✒ Direction in y-axis represents the unit vector j.

$\longmapsto\:\:\bf\purple{\vec{s}\:=\:0.5\hat{j}\:}$

$\bf\pink{We\:know\:that,}$

$\red\bigstar\:\:\bf{\color{peru}Work\:done\:=\:F\:.\:s\:}$

$:\implies\:\:\bf{Work\:done\:=\:(3\hat{i}\:+\:2\hat{j}\:+\:1\hat{k})\:.\:(0.5\hat{j})\:}$

$:\implies\:\:\bf{Work\:done\:=\:1.5\:(\hat{i}.\hat{j})\:+\:1\:(\hat{j}.\hat{j})\:+\:0.5\:(\hat{j}.\hat{k})\:}$

$:\implies\:\:\bf{Work\:done\:=\:1.5\times{0}\:+\:1\times{1}\:+\:0.5\times{0}\:}$

$:\implies\:\:\bf{Work\:done\:=\:0\:+\:1\:+\:0\:}$

$:\implies\:\:\bf\green{Work\:done\:=\:1\:joule}$

$\Large\bold\therefore$ A) The work done is 1 Joule.