A) 4 N
B) \[16\,N\]
C) 24 N
D) 96 N
Correct Answer: D
Solution :
The force of friction between the block m and the block\[M={{\mu }_{1}}\,mg.\]Force of friction between block M and the horizontal surface\[={{\mu }_{2}}(M+m)g.\]As there is no slipping between the blocks, so the entire system can be considered as a single system. Invoking Newton's second law on composite system. Thus,\[F=(M+m)a+{{\mu }_{2}}(M+m)g\] (1) Now, since the force on block m is \[{{\mu }_{1}}mg,\] its acceleration is \[a=\frac{{{\mu }_{1}}mg}{m}={{\mu }_{1}}g\] Using Eqs. (1) and (2), \[F={{\mu }_{1}}(M+m)g+{{\mu }_{2}}(M+m)g\]\[=({{\mu }_{1}}+{{\mu }_{2}})(M+m)g\] \[=(0.5+0.7)\times (5+3)\times 10=96\,N.\] Hence, the correction option is [d].
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