Question

The sum of two forces acting at a point is 16 N. If the resultant force is 8N and its direction is
perpendicular to the smaller force then the forces are
(1) 6 N and 10N (2) 8 N and 8 N (3) 4 N and 12 N (4) 2 N and 14 N​

Answer 1

Answer:

Option 1 ( 6 N and 10 N)

Explanation:

Let the force of smaller magnitude be A and the force of larger magnitude be B.

Here,it is clearly given that the resultant force is R perpendicular to small force. hence, we can say that b is the hyopetenuse .

Herefore, b² = R² + A²

=> R² = b² - A²

= 8²

= 64 .......................... ( 1 ).

Here, it is also given that

A + B = 16

therefore , B = 16 - A ..........................( 2 ).

Now, by substituting ( 2 ) in ( 1 ).we get,

( 16 - A ) ²- A² = 64

=> 256 - 32A + A² - A² = 64

32A = 256 - 64 = 192

A = 192 / 32

= 6

Hence, we get the result

B = 16 - A = 16 - 6 = 10

Therefore, the magnitude of the two vectors are 6 and 10.

==============

Follow me!

@Hⱥຮຮⱥnﾂℕk