Question

A body is projected up along a smooth inclined plane with velocity u from the point A as shown in Fig. The angle of inclination is ${45}^{\circ }$ 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 u? The length of inclined plane is $20\sqrt{2}m$.

• A. $40m{s}^{-1}$
• B. $40\sqrt{2}m{s}^{-1}$
• C. $20m{s}^{-1}$
• D. $20\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is D $20\sqrt{2}m{s}^{-1}$

A angle of projection from $B$ is ${45}^o$.

As the body is able to cross the well of diameter $40$m,hence.

$R=\frac{v^2}{g}$ or $v=\sqrt{gR}$=$\sqrt{10\times 40}=20m{s}^{-1}$on the inclined plane , the retardation is $g\sin \alpha =g\sin {45}^o=10/\sqrt{2}m{s}^{-2}$

Using $v^2-u^2=2ax$$(20{)}^2-u^2=2\times \left(\frac{10}{\sqrt{2}}\right)\times 20\sqrt{2}$$u=20\sqrt{2}m{s}^{-1}$