First slide

Application of Newtons laws

Question

In the figure shown if mass of each block is m. Find the acceleration of block A.
(use g=10 m/s²)

Moderate

A

2 m/s²
B

4 m/s²
C

1 m/s²
D

5 m/s²

Solution

Let acc. of block A be a_A and acc. of block B be a_B. Hence
$\begin{array}{l} 2 T = m a_{A} - - (1) \\ a n d \\ m g - 4 T = m a_{B} - - - (2) \end{array}$
Constrained Motion : $(2 T) a_{A} = (4 T) a_{B} (∵ T \propto \frac{1}{a})$
$\Rightarrow a_{A} = 2 a_{B}$
After solving we get,
$\begin{array}{l} f r o m 2 \times (1) a n d (2) \\ \Rightarrow 2 (2 T = m a_{A}) \\ \Rightarrow 4 T = 2 m a_{A} \\ \Rightarrow m g - 4 T = m \frac{a_{A}}{2} \\ o n s o l v i n g w e g e t \\ \Rightarrow m g = \frac{5 m a_{A}}{2} \\ \Rightarrow a_{A} = 4 m s^{- 2} \end{array}$

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