Question

Two masses 2 kg and 4 kg are connected at the two ends of a light inextensible string passing over a frictionless pulley. If the masses are released, then find the acceleration of the masses and the tension in the string.

• A. $a=3.33m/s^{2}T=25.55N$
• B. $a=4m/s^{2}T=30N$
• C. $a=4m/s^{2}T=25N$
• D. $a=3.33m/s^{2}T=26.67N$

Answer 1

The correct option is D $a=3.33m/s^{2}T=26.67N$

When the masses are released, then the masses move with common magnitude of acceleration a,
$a=\frac{M_1-M_2}{M_1+M_2}g$
Given, $M_1=4kg,M_2=2kg,g=10m/s^2$
$\therefore a=\frac{4-2}{4+2}\times 10=\frac{2}{6}\times 10=3.33m/s^2$
And tension T in the string is,
$T=\frac{2M_1{M}_2}{M_1+M_2}\times g$
$=\frac{2\times 4\times 2}{2+4}\times 10=\frac{16}{6}\times 10=26.67N$