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A cat of mass 5 kg is hanging on the table cloth (neglect the mass) and pulling a fishbowl of mass 11 kg towards the edge of the table. The coefficient of friction between the table cloth under the fish bowl and the table is 0.4. If the fish bowl is 1m from the edge of the table, how much time does it take for cat to pull the bowl off the table? ( take g = 9.8 $m s^{- 2}$ )

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\sqrt{5} s e c

$\sqrt{3} s e c$

$\sqrt{2} s e c$

2 sec

answer is B.

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Detailed Solution

From free body diagrams
X – component (bowl)

T - f = m_{b} a

Y – component (bowl)

N - m_{b} g = 0

Y – component (cat)

m_{c} g - T = m_{c} a

$a = \frac{(m_{c} - μ_{k} m_{b})}{m_{b} + m_{c}} = \frac{g}{15}$
Displacement

x = \frac{1}{2} a t^{2}; t = \sqrt{\frac{2 x}{a}} = \sqrt{3} s e c

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