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

A body of mass 10 kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is
(a) 1 m s^{-2}at an angle of \tan^{-1}\left ( \frac{4}{3} \right ) w.r.t. 6N force.
(b) 0.2 ms^{-2} at an angle of \tan^{-1}\left ( \frac{4}{3} \right ) w.r.t. 6N force.
(c) 1 ms^{-2} at an angle of \tan^{-1}\left ( \frac{3}{4} \right )w.r.t. 8N force.
(d) 0.2 ms^{-2} at an angle of \tan^{-1}\left ( \frac{3}{4} \right ) w.r.t. 8N force.

Answers (1)

Here we know that ,m = 10kg, F2 = 8N & F1 = 6N then,

Let's look at this figure to understand better. Here, R is the resultant force,

R =\sqrt{ 8^{2}+6^{2}} =\sqrt{64+36}=\sqrt{100}=10

Thus, R = 10 N

Now, we know that 

F = ma \rightarrow a = \frac{F}{m} = \frac{R}{m} = \frac{10}{10} = 1ms^{-2}      ………. (1)

So, tan \theta_{1} =\frac{8}{6} = \frac{4}{3}=\theta_{1} = \tan^{-1}\left (\frac{4}{3} \right )   ………… (2)

and, tan \theta_{2} =\frac{6}{8} = \frac{3}{4}=\theta_{2} = \tan^{-1}\left (\frac{3}{4} \right )       ……….. (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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infoexpert24

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