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Three blocks $$A$$, $$B$$ and $$C$$ are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tensions $$T_1$$ and $$T_2$$ in the string are respectively:
Let us write equations for all three blocks A,B and C
For A:-
$$F-T_2=2a$$
$$80-T_2=2a$$
For B:-
$$T_2-T_1=3a$$
and For C:-
$$T_1=5a$$
Now on adding all 3 equations
We get $$80\ =\ 10a$$
$$a = 8 \text{ m s}^{-2}$$
now substitute value of a in equation 1
$$80-T_2=2a$$
$$80-T_2=2\times\ 8$$
$$80-16\ =T_2$$
$$T_2=64N$$
Substitute the value of a in equation 3
$$T_1=5a$$
$$T_1=5\times\ 8$$
$$T_1=40N$$
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