Solve it buddies???

Question

H C Verma problems

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Answer 1 · 2017-08-18T12:50:23

See below.

For the object with mass $2 M$ $2M$

$T_{1} = 2 M a_{1}$ $T_1=2M a_1$

For the pulley $B$ $B$

$T_{1} = 2 T_{2}$ $T_1= 2T_2$

For the object with mass $M$ $M$

$M g - T_{2} = M a_{2}$ $M g - T_2 = M a_2$

Kinematic constraint

$a_{2} = 2 a_{1}$ $a_2 = 2 a_1$

Force actuating in pulley $A$ $A$

$F_{c} = \sqrt{2} T_{2}$ $F_c = sqrt 2 T_2$

Mounting now the system of equations

${(2 M a_1 = T_1), (T_1 = 2 T_2), (M g - T_2 = M a_2), (a_2 = 2 a_1), (F_c = sqrt[2] T_2):}$

and solving we get

${(T_1 = (2 g M)/3), (T_2 = (g M)/3), (a_1 = g/3), (a_2 = (2 g)/3), (F_c = 1/3 sqrt[2] g M):}$