Question

Two blocks A and B of the same mass are joined by a light string and placed on a horizontal surface. An external horizontal force $P$ acts on A. The tension in the string is $T$. The forces of friction acting on A and B are $F_1$ and $F_2$ respectively. The limiting value of $F_1$ and $F_2$ is $F_0$. As $P$ is gradually increased,

• A. for $P<F_0,T=0$
• B. for $P<2F_0,T=P-F_0$
• C. for $P>2F_0,T=\frac{P}{2}$
• D. none of the above

Answer 1

Answer: (A), (B), (C)

for $P<2F_0,T=P-F_0$
for $P<F_0,T=0$
for $P>2F_0,T=\frac{P}{2}$

Case (I) for $P<F_0$ , all the force will be opposed by friction on block A hence no tension in the string.

Case (II) for $P<{2F}_0$ , forced cancelled by a block friction is $F_0$ and rest of force is opposed by friction of second block. so tension in string is friction on B $=P-F_0$

Case (III) for $P>{2F}_0$ , $T=$ force for accln. of B $+$ force of friction on B

$T=\frac{P-2F_0}{2M}\times M+F_0=\frac{P}{2}$