Question

In the figure shown, $M_A=3kg,M_B=4kgand{M}_C=8kg$. Coefficient of friction between any two surfaces is 0.25. Pulley is frictionless and string is massless. A is connected to wall through a massless rigid rod. Which of the following option(s) is/are correct? (Take g = 10 $m{s}^{-2})$

• A. Value of F to keep C moving with constant speed is 80 N.
• B. Value of F to keep C moving with constant speed is 120 N.
• C. If F is 200 N, then acceleration of B is 10 $m{s}^{-2}$
• D. To slide C towards left, F should be at least 50 N.

Answer 1

Answer: (A), (C)

The correct options are
A Value of F to keep C moving with constant speed is 80 N.
C If F is 200 N, then acceleration of B is 10 $m{s}^{-2}$

Maximum value of friction between A and B is
$f_1{)}_{max}=0.25\times 3\times 10=7.5N$
Maximum value of friction between B and C is
$f_2{)}_{max}=0.25\times 7\times 10=17.5N$
and maximum value of friction between C and ground is
$f_3{)}_{max}=0.25\times 15\times 10=37.5N$
$F_0=$ force on A from rod

If C is moving with constant velocity, then B will also move with constant velocity
For B, T = 17.5 + 7.5 = 25 N
For C, F = 17.5 + 25 + 37.5 = 80 N
For F = 200 N
Acceleration of B towards right
= acceleration of C towards left
= a (say)
Then T – 7.5 – 17.5 = 4 a ...(i)
200 – 17.5 – 37.5 – T = 8a ….(ii) On solving these two equation, we get a =10 m/s²