Laws Of Motion Question 277
Question: Five persons A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and cart is moving with acceleration $ 3m/s^{2} $ in east direction. When person A stops pulling, it moves with acceleration $ 1m/s^{2} $ in the west direction. When person B stops pulling, it moves with acceleration $ \text{24 }m/s^{2} $ in the north direction. The magnitude of acceleration of the cart when only A and B pull the cart keeping their directions same as the old directions, is
Options:
A) $ \text{24 }m/s^{2} $
B) $ m\sqrt{71}m/s^{2} $
C) $ \text{30 }m/s^{2} $
D) $ \text{25 }m/s^{2} $
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Answer:
Correct Answer: D
Solution:
[d] When all are pulling
$ {{\vec{F}} _{net}}=100\times 3\hat{i}\text{}…..\text{(i)} $
When A stops $ {{\vec{F}} _{net}}-{{\vec{F}} _{A}}=100\times 1( -\hat{i} )….( ii ) $
From these three we get $ {{\vec{F}} _{A}}+{{\vec{F}} _{B}}=100( 7\hat{i}-24\hat{j} ) $
$ \therefore \text{Required }acc^{n}=\sqrt{7^{2}+{{( -24 )}^{2}}}=25\text{ m/}{{m}^{2}} $
