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Question

A body of mass 10 kg is acted upon by two perpendicular forces, 6 N and 8 N. The resultant acceleration of the body is

A
1 ms2, at an angle of tan1(43) with respect to 6 N force.
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B
0.2 ms2, at an angle of tan1(43) with respect to 6 N force.
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C
1 ms2, at an angle of tan1(34) with respect to 8 N force.
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D
0.2 ms2, at an angle of tan1(34) with respect to 8 N force.
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Solution

The correct options are
A 1 ms2, at an angle of tan1(43) with respect to 6 N force.
C 1 ms2, at an angle of tan1(34) with respect to 8 N force.
We have given mass m=10 kg, F2=8N, F1=6N.
Let's look at this figure to understand better.
Here, R is the resultant force
R=82+62=64+36=100=10 N
Now, we know F=ma or a=Fm=Rm=1010=1 ms2(1)
So, tan θ1=86=43; θ1=tan1 43 (2)
tan θ2=68=34; θ2=tan1 34 (3)

Hence from equations (1) & (2) option (a) is correct and from equations (1) & (3) option (c) also our acceleration is different hence options (b) & (d) are wrong.

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