The coefficient of friction between two blocks is 0.5. The masses of blocks A and B are 1 kg and 2 kg respectively .Which of the given statements is /are correct?

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If $F = 5 N$ , the friction on block B is 3.33 N in rightward direction.

If $F = 15 N$ , the acceleration of block A is 10 m/s²

If $F = 6 N$ , the friction on block A is 4 N

If $F = 6 N$ , the friction on block A is 5 N

answer is A, B, C.

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Detailed Solution

(ABC)
SOL.: The common acceleration of the system is $a_{0} = \frac{F}{3}$ . From free body diagram of block A in the frame of block B,
Question Image
The net applied force is $F - m_{A} a_{0} \leq μ m_{A} g$
$\Rightarrow$ Block move with common acceleration and the friction is static.
If $F - m_{A} a_{0} > μ m_{A} g$
$\Rightarrow$ Block have relative motion between them and friction is kinetic.
(a) Here, $F - m_{A} a_{0} = 5 - \frac{5}{3} = \frac{10}{3} N$
And $f_{\max} = μ m_{A} g = 4 N$
$∴$ $F - m_{A} a_{0} < f_{\max}$ common acceleration and friction is static,
$∴$ $a_{0} = \frac{5}{3} m / s^{2}$