Two smooth inclined planes A and B each of he | vedclass

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

Question

(C) The length of an inclined plane of height $h$ and angle $	heta$ is $L = \frac{h}{\sin 	heta}$.The acceleration of a block sliding down a smooth

Vedclass · Accepted Answer

$4\left(\frac{\sqrt{3}-1}{\sqrt{3}}\right) \ s$

Vedclass · Answer

(C) The length of an inclined plane of height $h$ and angle $	heta$ is $L = \frac{h}{\sin 	heta}$.The acceleration of a block sliding down a smooth inclined plane is $a = g \sin 	heta$.Using the equation of motion $s = ut + \frac{1}{2}at^2$,where $u = 0$ and $s = L$:$L = \frac{1}{2} (g \sin 	heta) t^2 \implies \frac{h}{\sin 	heta} = \frac{1}{2} g \sin 	heta \ t^2$.Thus,$t = \sqrt{\frac{2h}{g \sin^2 	heta}} = \frac{1}{\sin 	heta} \sqrt{\frac{2h}{g}}$.Given $h = 20 \ m$ and $g = 10 \ m \ s^{-2}$,we have $\sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 20}{10}} = 2 \ s$.For plane $A$ $(	heta_1 = 30^{\circ})$: $t_1 = \frac{1}{\sin 30^{\circ}} 	imes 2 = \frac{1}{0.5} 	imes 2 = 4 \ s$.For plane $B$ $(	heta_2 = 60^{\circ})$: $t_2 = \frac{1}{\sin 60^{\circ}} 	imes 2 = \frac{1}{\sqrt{3}/2} 	imes 2 = \frac{4}{\sqrt{3}} \ s$.Therefore,$t_1 - t_2 = 4 - \frac{4}{\sqrt{3}} = 4 \left( 1 - \frac{1}{\sqrt{3}} ight) = 4 \left( \frac{\sqrt{3}-1}{\sqrt{3}} ight) \ s$.

Similar Questions

$A$ frictionless wire $AB$ is fixed on a circle of radius $R$. $A$ very small bead slips on this wire. The time taken by the bead to slip from $A$ to $B$ is:

As per the given figure,a weightless pulley $P$ is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if $g = 10 \, m/s^2$):

$A$ truck of mass $10000 \ kg$ is moving up an inclined plane with a length of $50 \ m$ and a height of $1 \ m$ at a speed of $36 \ km/h$. What is the power of the engine in $kW$?

Block $A$ of weight $100 \, N$ rests on a frictionless inclined plane of slope angle $30^{\circ}$. $A$ flexible cord attached to $A$ passes over a frictionless pulley and is connected to block $B$ of weight $w$. Find the weight $w$ for which the system is in equilibrium.

Vedclass Test Series

Exam Paper Generator

Online Exam Module