Q. Two masses 8 kg and 12 kg are connected at the two ends of a string that goes over a frictionless pulley. Calculate the acceleration of the masses and the tension in the string. $(Take\ g = 10\ m/s^{2})$
A) $8\ m/s^{2}$, 144 N
B) $4\ m/s^{2}$, 112 N
C) $6\ m/s^{2}$, 128 N
D) $2\ m/s^{2}$, 96 N
Explanation
(d) Equations of motion are
$m_{1}a = T - m_{1}g$
$and\ \ m_{2}a = m_{2}g - T$
$\Longrightarrow \ \ 8a = T - 8g\ \ \ \ldots.(i)$
$12a = 12g - T\ \ldots.(ii)$
Form Eqs. (i) and (ii), we get
$a = \frac{g}{5} = 2\ {m/s}^{2}$
Substituting the value of $a$ in Eq.(i)
We get $T =$ 96 N
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.