A wooden block of mass m1 kg accelerates at 10 ms–2 when a force of 5 N acts on it. Another block of mass m2 kg accelerates at 20 ms–2 when same force acts on it. Find the acceleration if both the blocks are tied together and same force acts on their combination :

Foundation

Physics Foundation

Force and Newtons Law of Motion

Question

A wooden block of mass m₁ kg accelerates at 10 ms^–2 when a force of 5 N acts on it. Another block of mass m₂ kg accelerates at 20 ms^–2 when same force acts on it. Find the acceleration if both the blocks are tied together and same force acts on their combination :

4.67 ms^–2

none of these

1.67 ms^–2

6.67 ms^–2

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(a)

(b)

        (c)
   From (a)
$F = M_{1} a_{1}, M_{1} = \frac{5}{10} = 0 .5 kg$
   From (b)
$F = M_{2} a_{2}, M_{2} = \frac{5}{20} = 0 .25 kg$
   From (c)
$F = (0 .5 + 0 .25) a, a = \frac{5}{0 .75} = 6 .67 m / s^{2}$