Question

The two forces when acting at right angle to each other, produces a resultant force of ✓10N and when at 60°, produce a resultant of ✓13 N. These forces are:
a.) 3N and 1N
b.) ✓5N and ✓5N

Answer 1

as ab = 3 then only integer possible values are 3×1
therefore option a is correct


PLEASE REFER ABOVE ATTACHMENT

Answer 2

Given:

The two forces when acting at a right angle to each other produce a resultant force of ✓10N

When at 60°, they produce a resultant of ✓13 N

To Find:

The magnitude of both the forces

Solution:

The forces are a.) 3N and 1N.

Two vectors of magnitude A and B inclined to one another at an angle ∅ produce a resultant R.

According to the vector formula,

|R| = √ (A²+B²+2ABcos∅)

In case one,

∅ = 90°

⇒ R1 = √ (A²+B²+2ABcos90°)

Or ✓10N = √ (A²+B²+2ABcos90°)

Substituting cos90° = 0,

✓10N = √ (A²+B²)

Squaring both the sides we get

10 N = A²+B²    - (1)

Case two:

R2 = √ (A²+B²+2ABcos60°)

Or ✓13 N = √ (A²+B²+2ABcos60°)

Substituting cos60° = 1/2,

✓13 N = √ (A²+B²+AB)

Squaring both the sides we get

13 N = (A²+B²+AB)   - (2)

Substituting equation 1 in equation 2,

13 = 10 + AB

or AB = 3     - (3)

Out of the given options, only a satisfies equation 3 ( 3 X 1 = A X B = 3)

Hence, The forces are a.) 3N and 1N.