Question

In the figure, a man of true mass M is standing on a weighing machine placed in a cabin. The cabin is joined by a string with a body of mass m. Assuming no friction, and negligible mass of cabin and weighing machine, the measured mass of man is:

• A. $\frac{Mm}{M+m}$
• B. $\frac{Mm}{M-m}$
• C. M
• D. depends on g

Answer 1

The correct option is A $\frac{Mm}{M+m}$

weight measure by weighting machine $=M(g-a)$

from F.B.D of lift

$T=m(g-a)$.....(1)

from F.B.D of pully

$T=ma$......(2)

$ma=m(g-a)$

$mg=ma+ma$

$mg=a(m+m)$

$a=\frac{M}{m+m}g$

$weight=m(g-a)$

$=m(g-\frac{mg}{m+m})$

$=\frac{m(m+m-m)g}{m+m}$

$w=\frac{mmg}{m+m}$

$mass=\frac{mm}{m+m}$