Two forces 
and 
are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between 
and 
is 
. The value of 
is ________.
Text Solution
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Let's denote the magnitude of the smaller force as F, hence the magnitude of the larger force is 3F. The resultant force 
is equal in magnitude to the larger force, which means 
. When two forces 
and 
act on a body, the magnitude of their resultant 
can be found using the law of vector addition:
where 
is the angle between 
and 
. Given that in our case 
and 
, by substituting these values into the equation, we get:
Simplifying this equation by subtracting 
from both sides gives:
Dividing both sides by 
gives:
Therefore, 
.
It is given that the angle between 
and 
is 
, hence comparing this with the above result, we find that 
. Therefore, 
.
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