First slide

Connected bodies

Question

In the diagram shown in figure, match the following columns. (Take, g = 10 ms^-2)

Column I
(A) Acceleration of 2 kg block
(B) Net force on 3 kg block
(C) Normal reaction between 2kg and 1 kg
(D) Normal reaction between 3 kg and 2 kg
Column II
(p) 8 SI unit
(q) 25 SI unit
(r) 2 SI unit
(s) 45 N
(t) None

Moderate

A

A B C D
q r t t
B

A B C D
p s r t
C

A B C D
s s p t
D

A B C D
r t q t

Solution

Acceleration of system,
$a = \frac{60 - 18 - (m_{1} + m_{2} + m_{3}) g \sin 30 °}{(m_{1} + m_{2} + m_{3})} = 2 {ms}^{- 2}$
Net force on 3 kg block $= m_{3} a = 6 N$
From free body diagram of 1 kg block, we have
$N_{12} - m_{1} g \sin 30 ° - 18 = m_{1} a$
$\Rightarrow N_{12} = 25 N$
From free body diagram of 3 kg block, we have
$60 - m_{3} g \sin 30 ° - N_{32} = m_{3} a$
$∴ N_{32} = 39 N$
Hence, $A \to r, B \to t, C \to q, D \to t$

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