Question

Two blocks of masses 4 kg and 1 kg are hanging with the
help of two ideal strings A and B as shown in the figure. The
tension in the string B will be [g = 10 m/s2]
a) 10N
b) 50N
c) 30N
d) 40N​

Answer 1

Given:

Two blocks of masses 4 kg and 1 kg are hanging with the help of two ideal strings A and B as shown in the figure.

To find:

Tension in string B;

Diagram:

$\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(2,2){\line(0,1){2}}\put(2,4){\line(1,0){2}}\put(4,4){\line(0,-1){2}}\put(4,2){\line(-1,0){2}}\put(3,3){\vector(0,1){2}}\put(3.25,5){ T_{A} }}\put(3,3){\vector(0,-1){2}}\put(3.25,1){ 1g+T_{B} }\put(3.25,3){1\:kg}\put(1.5,0){ \rm{\underline{FBD\:of\:1\:kg}} }\end{picture}$

$\setlength{\unitlength}{1cm}\begin{picture}(6,6)\put(2,2){\line(0,1){2}}\put(2,4){\line(1,0){2}}\put(4,4){\line(0,-1){2}}\put(4,2){\line(-1,0){2}}\put(3,3){\vector(0,1){2}}\put(3.25,5){ T_{B} }}\put(3,3){\vector(0,-1){2}}\put(3.25,1){4g}\put(3.25,3){4\:kg}\put(1.5,0){ \rm{\underline{FBD\:of\:4\:kg}} }\end{picture}$

Calculation:

According to FBD of 1 kg mass;

$T_{A} = (1 \times g) + T_{B}$

$= > T_{A} = 10 + T_{B} \: \: \: .....(1)$

According to FBD of 4 kg block;

$T_{B} = (4 \times g)$

$\boxed{ = > T_{B} = 40 \: N}$

Putting value of T_(B) in eq.(1), we get:

$= > T_{A} = 10 + T_{B}$

$= > T_{A} = 10 + 40$

$\boxed{=> T_{A}=50 N}$

So, value of T_(B) = 40 N