Question

The sum of magnitude of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force then the forces are
O 6 Nand 10 N
08 N and 8 N
04 N and 12 N
O2 N and 14 N​

Answer 1

Answer:

• Two forces would be 6 N and 10 N

Correct option is (a)

Explanation:

Let, two vector forces acting on a point be A and B

then, sum of their magnitudes will be

• A + B = 16 N

And, Let their resultant force be R

then, magnitude of their resultant force is

• R = 8 N

It is given that,

• Resultant force is perpendicular to the minimum force
• Let, A be the minimum force

so,

Vectors A , B and R will make a right angled triangle such as B will be hypotenuse, A and R being other two sides.

[ Vector A will be minimum force and will be perpendicular to R ]

Hence, Using Pythagoras theorem

→ B² = A² + R²

→ ( 16 - A )² = A² + ( 8 )²

→ 256 + A² - 32 A = A² + 64

→ 32 A = 256 - 64

→ 32 A = 192

→ A = 6 N

so,

Minimum force is 6 N

hence, second force will be ( 16 - 6 ) = 10 N

Therefore,

• Two forces are 6 N and 10 N .

OPTION (a) is correct.