4. The simple sum of two forces acting at a point is 16 N and their vector sum is 8 N and its
direction is perpendicular to the smaller force, then the forces are
a. 6 N and 10 N
C. 8 N and 8 N
b. 4 N and 12 N
d. 2 N and 14 N
5. A particle moves in a circularpath with decreasing speed. Choose the correct statement
Answers
Answer:
8 Ñ and 8 N
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I think this is the correct answer any way
Given : The simple sum of two forces acting at a point is 16 N and their vector sum is 8 N and its direction is perpendicular to the smaller force,
To Find : the forces are
a. 6 N and 10 N
C. 8 N and 8 N
b. 4 N and 12 N
d. 2 N and 14 N
Solution:
Let say two forces are
(16 - A) N along x axis
and A N at angle α
A > 16 - A
As Resultant direction is perpendicular to the smaller force,
Hence
A sin α = 8
16 - A + A Cosα = 0
=> A Cosα = A - 16
A sin α = 8
A Cosα = A - 16
Squaring and adding
A² = 64 + A² + 256 - 32A
=> 32A = 320
=> A = 10
Hence 16- A = 6
Forces are 10 N and 6 N
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