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Question 11 Mark

A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle.

Answer

At the highest point of a vertical circle

$\frac{\text{mv}^2}{\text{R}}=\text{mg}$

$\Rightarrow\text{v}^2=\text{Rg}\Rightarrow\text{v}=\sqrt{\text{Rg}}$

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Question 21 Mark

A scooter weighing 150kg together with its rider moving at 36km/ hr is to take a turn of radius 30m. What horizontal force on the scooter is needed to make the turn possible?

Answer

Given that m = 150kg.

v= 36km/ hr = 10m/ sec, r = 30m.

Horizontal force needed is

$\frac{\text{mv}^2}{\text{r}}=\frac{150\times(10)^2}{30}$

$\frac{150\times100}{30}=500\text{N}$

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Question 31 Mark

Is it necessary to express all angles in radian while using the equation $\omega=\omega_0+\text{at}?$

Answer

No, we do not need to express all the angles in radian we can take limit over very small angle and calculate it over the radian.

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