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Standard XII

Physics

Relative Velocity

Three blocks ...

Question

Three blocks A, B and C are connected together with the help of strings as shown in figure. The masses are respectively 10 kg, 30 kg and 50 kg. They are pulled by a force of 18 N on a frictionless horizontal surface. Calculate the following:
(i) Tension $T_{1}$ in the first string
(ii) Tension $T_{2}$ in the second string and
(iii) Acceleration of the blocks.

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Solution

Acceleration of the blocks $a = \frac{F}{m_{1} + m_{2} + m_{3}}$
$⟹ a = \frac{18}{10 + 30 + 50} = 0.2 m / s^{2}$
Block of mass $m_{1}$ :
Using $18 - T_{1} = m_{1} a$
Or $18 - T_{1} = 10 \times 0.2$
$⟹ T_{1} = 16 N$
Block of mass $m_{3}$ :
Using $T_{2} = m_{3} a$
Or $T_{2} = 50 \times 0.2 = 10 N$

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Acceleration of the blocks a=Fm1+m2+m3⟹ a=1810+30+50=0.2 m/s2Block of mass m1 :Using 18−T1=m1aOr 18−T1=10×0.2⟹ T1=16 NBlock of mass m3 :Using T2=m3aOr T2=50×0.2=10 N