Tardigrade
Question
Physics
An insect crawls up a hemispherical surface very slowly (see the figure-3.114 ). The coefficient of friction between the insect and the surface is 1 / 3. If the line joining the centre of the hemispherical surface to the insect makes an angle α with the vertical, the maximum possible value of α is given by :

Q. An insect crawls up a hemispherical surface very slowly (see the figure-$3.114$ ). The coefficient of friction between the insect and the surface is $1 / 3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by :

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$\cot \alpha=3$

70%

$\tan \alpha=3$

10%

$\sec \alpha=3$

20%

$\text{cosec} \alpha=3$

Solution:

For equilibrium of insect we use
$m g \sin \alpha=f$
$m g \sin \alpha=\mu N=\mu m g \cos \alpha$
$\tan \alpha=\mu=\frac{1}{3}$
$\cot \alpha=3$

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$\cot \alpha=3$

$\tan \alpha=3$

$\sec \alpha=3$

$\text{cosec} \alpha=3$

For equilibrium of insect we use $m g \sin \alpha=f$ $m g \sin \alpha=\mu N=\mu m g \cos \alpha$ $\tan \alpha=\mu=\frac{1}{3}$ $\cot \alpha=3$

Questions from Work, Energy and Power

1. The work done by a particle moving with a velocity of $0.7\, c$ (where c is the velocity of light) in empty space free of electromagnetic field and far away from all matter is:

2. The machine gun fires $240 \, $ bullets per minute. If the mass of each bullet is $10 \, g$ and the velocity of the bullets is $600 \, m \, s^{- 1}$ ,the power (in $kW$ )of the gun is

4. A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_{c}$ is varying with time $t$ as $a_{c}=k^{2} \, rt^{2}$ , where $k$ is a constant. The power delivered to the particle by the force acting on it is

5. A ball of mass $1\, kg$ collides with a wall with speed $8\, ms ^{-1}$ and rebounds on the same line with the same speed. If mass of the wall is taken as infinite, the work done by the ball on the wall is

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2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

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5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ? (density of mercury $= 13600 kg/m^{3})$

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For equilibrium of insect we use
$m g \sin \alpha=f$
$m g \sin \alpha=\mu N=\mu m g \cos \alpha$
$\tan \alpha=\mu=\frac{1}{3}$
$\cot \alpha=3$

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$