A cart has mass 2 metric ton and sand of 1 metric ton is inside the cart. Now a force of 10 N is applied on cart and sand starts to leak with rate of 0.5 kg/s. What is the velocity of cart when total sand has come out from the cart ?

Question

A cart has mass 2 metric ton and sand of 1 metric ton is inside the cart. Now a force of 10 N is applied on cart and sand starts to leak with rate of 0.5 kg/s. What is the velocity of cart when total sand has come out from the cart ? (A) 13.86 m/s (B) 0.06 m/s (C) 2.81 m/s (D) 18.01 m/s

Tardigrade Admin · Accepted Answer

Mass of the cart with sand changes then its acceleration also changes.

a = \frac{F}{m} = \frac{F}{m _{0} - μ t}

where m is mass of system at time t,

m = m_{0} - μ t

a = \frac{F}{m _{0} - μ t}

or

\frac{d v}{d t} = \frac{F}{m _{0} - μ t}

\int_{0}^{v}

dv=F

\int_{0}^{t}

\frac{d t}{m _{0} - μ t}

v = \frac{F}{μ} in (\frac{m _{0}}{m _{0} - μ t})

Here F = 10 N; μ = 0.5 kg/s
m₀ = 2 metric tone
m₀ - μt = 1 metric tone

∴ v = \frac{10}{0.5} in (2) = 20 \times 0.693 = 13.86

m/s

Q. A cart has mass 2 metric ton and sand of 1 metric ton is inside the cart. Now a force of 10 N is applied on cart and sand starts to leak with rate of 0.5 kg/s. What is the velocity of cart when total sand has come out from the cart ?

13.86 m/s

0.06 m/s

2.81 m/s

18.01 m/s