Question

A sphere of mass m is kept between two inclined walls, as shown in the figure. All surfaces are smooth, then the ratio of normal reaction $\left(N_1/N_2\right)$ offered by the walls 1 and 2 on the sphere will be:

• A. $tan\theta$
• B. $tan2\theta$
• C. Both A and B
• D. None of above

Answer 1

The correct option is D None of above

$Given$ :- Mass of sphere = ( $m$ )

$ToFind$ :- Ratio of normal reaction $\left(\frac{N_1}{N_2}\right)$

$Solution$ :- Since , the sphere is in rest position ,

$\therefore$ $\sum f_x=0$ ( Net horizontal force )

$⟹$ $N_{2}cos\theta =N_{1}cos\theta$

$\therefore$ $\underset{–}{\frac{N_1}{N_2}=\frac{1}{1}}$

Hence , $\underset{–}{OptionD\left(Noneoftheabove\right)iscorrect.}$