Question

Find the relation between the acceleration of sphere $\left(a\right)$ and acceleration of wedge $\left(b\right)$ in the figure shown

• A. $a=\frac{b\cos \alpha }{\cos \beta }$
• B. $a=\frac{b\cos \beta }{\cos \alpha }$
• C. $a=\frac{b{\cos }^2\beta }{\sin \alpha }$
• D. $a=\frac{b{\sin }^2\beta }{\cos \alpha }$

Answer 1

The correct option is A $a=\frac{b\cos \alpha }{\cos \beta }$

The acceleration of the bodies perpendicular to the surface of contact are equal as both the bodies should not loose the contact with each other, hence by figure we have
$\Rightarrow a\cos \beta =b\cos \alpha$

$\Rightarrow a=\frac{b\cos \alpha }{\cos \beta }$

Hence option A is the correct answer