Question

A body is projected up a smooth inclined plane with velocity V from the point A as shown in the figure. The angle of inclination is $45^o$ and the top is connected to a well of diameter $40$ m. If the body just manages to cross the well, what is the value of $V$? Length of inclined plane is $20\sqrt{2}m$.

• A. $40m{s}^{-1}$
• B. $40\sqrt{1}m{s}^{-1}$
• C. $20m{s}^{-1}$
• D. $20\sqrt{1}m{s}^{-1}$

Answer 1

Answer: (D)

Angle of projection from B is $45^o$. As the body is able to cross the well of diameter $40$ m, hence

or $R=\frac{v^2}{g},orv=\sqrt{gR}$

$v=\sqrt{10\times 40}-20m{s}^{-1}$

On the inclined plane, the retardation is:

g sin $\alpha =g$ sin $45^o=\frac{10}{\sqrt{2}}m{s}^{-2}$

Using $v^2-u^2=2ax$

$(20{)}^2-u^2=2\times (-\frac{10}{\sqrt{2}})\times 20\sqrt{2}$

$u=20\sqrt{2}m{s}^{-1},$
i.e., $v=20\sqrt{2}m{s}^1$