Question

Three equal weighs of mass $2kg$ each are hanging on a string passing over a fixed pulley as shown in the figure. The tension in the string connecting the weights $B$ and $C$ is

• A. Zero
• B. $13N$
• C. $3.3N$
• D. $19.6N$

Answer 1

The correct option is B $13N$

Let us take the tension between A and B be T and tension between B and C be $T_1$.

The masses are connected to a massless string moving over a frictionless pulley.

Now, if they are allowed to move freely, then they move with common magnitude of acceleration 'a'.

Mass of A, B and C = 2kg (m)

Now,

For C,

=> $ma=mg-T_1$

=> $T_1=mg-ma$. ....(1)

For B,

=> $ma=mg+T_1-T$. ....(2)

For A,

=> $ma=T-mg$

=> $T=ma+mg$. ....(3)

Now, from (1) and (3) we will put value of The and $T_1$ in (2), we get

=> $ma=mg+(mg-ma)-(ma+mg)$

=> $ma=mg+mg-ma-ma-mg$

=> $3ma=mg$

=> $a=g/3$

Now, putting the value in (1) and (3), we will get the tensions..

Tension between B and C = $m(g-a)$

= $m(g-g/3)$= $2\left(2g/3\right)$= $4g/3$= $40/3$ = $13.3N$