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Five persons A, B, C, D & E are pulling a cart of mass 100kg on a smooth surface and cart is moving with acceleration $3 m / s^{2}$ in east direction. When person 'A' stops pulling, it moves with acceleration $1 m / s^{2}$ in the west direction. When person 'B' stops pulling, it moves with acceleration $24 m / s^{2}$ in the north direction. The magnitude of acceleration of the cart when only A & B pull the cart keeping their directions same as the old direction is

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$3 \sqrt{71} m / s^{2}$

$30 m / s^{2}$

$26 m / s^{2}$

$25 m / s^{2}$

answer is C.

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Detailed Solution

$\bar{F_{A}} + \bar{F_{B}} + \bar{F_{C}} + \bar{F_{D}} + \bar{F_{E}} = 100 \times 3 i \to 1$

$\bar{F_{B}} + \bar{F_{C}} + \bar{F_{D}} + \bar{F_{E}} = 100 (- i) \to 2$

$\bar{F_{A}} + \bar{F_{C}} + \bar{F_{D}} + \bar{F_{E}} = 100 (24 j) \to 3$

$(1) - (2) \bar{F_{A}} = 400 i$

$(1) - (3); \bar{F_{B}} = 300 i - 2400 j$

$\bar{F_{A}} + \bar{F_{B}} = 700 i - 2400 j$

$| \bar{F_{A}} + \bar{F_{B}} | = \sqrt{700^{2} + 2400^{2}} = 2500 a = \frac{2500}{100} = 25$

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