Question

A cart loaded with sand moves along a horizontal plane due to a constant force F in the direction of velocity. Through a small hole in the bottom sand spills out at m kgs^-1. Find the velocity of the cart at any time t. Initial mass of the cart is m₀.

• A. $\frac { F } { m } \log _ { e } \frac { m _ { 0 } } { m _ { 0 } - m t }$
• B. $\frac { F } { m _ { 0 } } \log _ { e } \frac { m _ { 0 } } { m _ { 0 } - m t }$
• C. $\frac { \mathrm { F } } { \mathrm { m } _ { 0 } }$ t
• D. $\frac { \mathrm { F } } { \mathrm { m } }$ t

Answer 1

Answer: (A)

$\frac { F } { m } \log _ { e } \frac { m _ { 0 } } { m _ { 0 } - m t }$

Answer 2

Mass of the cart at any instant is m₀ – mt

acceleration a = $\frac { d v } { d t } = \frac { F } { m _ { 0 } - m t }$

v = $\int _ { 0 } ^ { t } \frac { F } { m _ { 0 } - m t } d t = \frac { F } { m } \log _ { e } \frac { m _ { 0 } } { m _ { 0 } - m t }$ .