Question

A trolley is under the action of a constant force F. The sand contained by it is poured out through a hole in the floor at the rate of m per second. If initial mass of sand and trolley was M and initial speed was u, then acceleration of trolley is given by

• A. $\frac { \mathrm { F } } { \mathrm { M } - \mathrm { mt } }$
• B. $\frac { \mathrm { F } } { \mathrm { M } + \mathrm { mt } }$
• C. $\frac { F } { M - m }$
• D. $\frac { F } { M + m }$

Answer 1

Answer: (A)

$\frac { \mathrm { F } } { \mathrm { M } - \mathrm { mt } }$

Answer 2

Instantaneous acceleration,

a = $\frac { \mathrm { dv } } { \mathrm { dt } } = \frac { \text { Constant force } } { \text { Instantaneous mass } }$

or a = $\frac { \mathrm { F } } { \mathrm { M } - \mathrm { mt } }$

( rate of fall os sand per second is m)