A body of mass 10kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is
A
1ms–2, at an angle of tan–1(43) with respect to 6N force.
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B
0.2ms–2, at an angle of tan–1(43) with respect to 6N force.
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C
1ms–2, at an angle of tan–1(34) with respect to 8N force.
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D
0.2ms–2, at an angle of tan–1(34) with respect to 8N force.
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Solution
The correct options are A1ms–2, at an angle of tan–1(43) with respect to 6N force. C1ms–2, at an angle of tan–1(34) with respect to 8N force. We have given mass m=10kg,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=10N Now, we know F=ma or a=Fm=Rm=1010=1ms−2……(1) So, tanθ1=86=43;θ1=tan−143……(2) tanθ2=68=34;θ2=tan−134……(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.