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A body of mass 5 kg is acted upon by two...

A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N Give the magnitude and direction of the acceleration of the body.

Text Solution

Verified by Experts

Here m = 5 kg
`F_1` = 8N and `F_2` = 6 N
The resultant force on the body
F = `sqrt (F_1^(2) + F_2^(2))` = `sqrt (8^(2) + 6^(2))` N
`implies` F = `sqrt ( 64 + 36 ) ` N = 10 N
The acceleration , a = F / m
`implies` a = 10 / 5 = 2 `ms^(-2)` in the same direction as the resultant force.
The direction of acceleration ,
tan`beta` = 6/8 = 3/4 = 0.75
or, `beta` = `tan^(-1)`(0.75)
= `37^(@)` with 8 N force.
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Knowledge Check

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