Question

A force F = 3i + 2j +4k displace an object from a point P (1,1,1) to another point of co-ordinate (2,0,3) . The work done by the force is
(a) 10 J
(b) 13 J
(c) 12 J
(d) None of these ​

Answer 1

Answer:

(b) 13 J is the required optiòn

Explanation:

According to the Question

It is given that

• F = 3i + 2j + 4k

we need to calculate the work done by the fòrce .

Let OA= i+ j+ k

And , OB = 2i+ 0j+ 3k

Now, calculating the displacement .

➻ displacement = Final position - Initial position

➻ S = OB - OA

➻ S = (2i+ 0j+ 3k) - (3i + 2j + 4k )

➻ S = i - j + 3k

So, the displacement is i- j + 3k

Now,

F= 3i + 2j + 4k

S = i - j+ 3k

----------------------

F.S = 3×1 + 2×1 + 4×2

F.S = 3 + 2 + 8

F.S = 13 J

• Hence, the work done by fòrce is 13 J

So , the required option is (b) 13 J.

Answer 2

Question

A force F = 3i + 2j +4k displace an object from a point P (1, 1, 1) to another point of co-ordinate (2, 0, 3). The work done by the force is :

• (a) 10 J
• (b) 13 J
• (c) 12 J
• (d) None of these

Answer

• Option (b) 13 J is correct.

Step By Step Explanation

Given

• Force = 3i + 2j + 4k
• Initial point = (1, 1, 1)
• Final point = (2, 0, 3)

To Find

• Work done by the force?

Solution

• Firstly, let's calculate it's displacement, we know that :

$\pmb{\boxed{\bf{Displacement = Final\:point - Initial\:point}}}$

⇒ Displacement = (2-1)i + (0-1)j + (3-1)k

⇒ Displacement = 1i + (-1)j + 2k

⇒ Displacement = 1i - 1j + 2k

➦ Displacement = i - j + 2k

∴ Hence, displacement is i - j + 2k.

• Now, let's calculate work done by force, we know that :

$\pmb{\boxed{\bf{Work\:done = Force\:.\:Displacement}}}$

↦ Work done = (3i + 2j + 4k) . (i - j + 2k)

↦ Work done = (3 × 1) + (2 × 1) + (4 × 2)

↦ Work done = 3 + 2 + 8

➡ Work done = 13 J

∴ Hence, work done by force is 13 J. So, Option (b) 13 J is correct.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬