There is a trolley in which there is a fixed inclined surface on which a smooth block of mass $5 \mathrm{kg}$ is placed. Two horizontal forces of magnitude $F_1$ and $F_2$ are applied on the trolley as shown to keep the trolley at rest. The value of $F_1 - F_2$ is : (Assume there is no friction between the trolley and horizontal ground and $g = 10 \mathrm{m} {\mathrm{s}}^{-2}$)

• A

  $0 \mathrm{N}$

   
• B

  $24 \mathrm{N}$
• Correct answer
  C

  $-24 \mathrm{N}$
• D

  $-30 \mathrm{N}$

   

Solution

There is a trolley for which

$F_1+N\sin 37°=F_2$




$F_1-F_2=\left[-N\sin 37°\right]$. . . (1)

$N\mathrm{=}\left[mg\cos 37°\right]$. . . (2)

$F_1-F_2=-mg\cos 37°\sin 37°$

$=-5\times 10\times \frac{4}{5}\times \frac{3}{5}=-24 \mathrm{N}$

Hence, the correct answer is option: 'C'.