An insect crawls up a hemispherical surface v | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the mass of the insect be $m$. The forces acting on the insect are:$1$. Weight $mg$ acting vertically downwards.$2$. Normal reaction $N$ actin

Vedclass · Accepted Answer

$\cot\,\alpha = 3$

Vedclass · Answer

(A) Let the mass of the insect be $m$. The forces acting on the insect are:$1$. Weight $mg$ acting vertically downwards.$2$. Normal reaction $N$ acting radially outwards from the centre.$3$. Frictional force $f$ acting tangentially upwards along the surface.Resolving the weight $mg$ into two components:- Along the radius: $mg \cos \alpha$ (acting inwards).- Tangential to the surface: $mg \sin \alpha$ (acting downwards).For equilibrium in the radial direction:$N = mg \cos \alpha$For equilibrium in the tangential direction:$f = mg \sin \alpha$Since the insect is crawling very slowly,the frictional force is at its maximum limit,$f = \mu N$.Substituting the expressions for $f$ and $N$:$\mu N = mg \sin \alpha$$\mu (mg \cos \alpha) = mg \sin \alpha$$\mu = 	an \alpha$Given $\mu = 1/3$,we have:$	an \alpha = 1/3$$\cot \alpha = 3$

Similar Questions

Identify the non-narcotic analgesic from the following.

When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \, cm$ or $100 \, cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $ \, Hz$)

The instantaneous values of alternating current and voltage in a circuit are given as $i = \frac{1}{\sqrt{2}} \sin(100\pi t) \text{ A}$ and $e = \frac{1}{\sqrt{2}} \sin(100\pi t + \frac{\pi}{3}) \text{ V}$. The average power in Watts consumed in the circuit is:

The heating of $NH _4 NO _2$ at $60-70^{\circ} C$ and $NH _4 NO _3$ at $200-250^{\circ} C$ is associated with the formation of nitrogen containing compounds $X$ and $Y$, respectively. $X$ and $Y$, respectively, are

Which one of the following complexes will have four isomers?

Vedclass Test Series

Exam Paper Generator

Online Exam Module