A block is kept on a fixed smooth wedge whose | vedclass

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

Question

(C) The slope of the curve at any point is given by $\frac{dy}{dx} = 	an 	heta$.Given $y = \frac{x^2}{\sqrt{3}}$,we have $\frac{dy}{dx} = \frac{2x}{

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) The slope of the curve at any point is given by $\frac{dy}{dx} = 	an 	heta$.Given $y = \frac{x^2}{\sqrt{3}}$,we have $\frac{dy}{dx} = \frac{2x}{\sqrt{3}}$.At the release point,$y = \frac{1}{4\sqrt{3}}$,so $\frac{x^2}{\sqrt{3}} = \frac{1}{4\sqrt{3}}$,which gives $x^2 = \frac{1}{4}$,or $x = \frac{1}{2}$.Substituting $x = \frac{1}{2}$ into the slope equation: $	an 	heta = \frac{2(1/2)}{\sqrt{3}} = \frac{1}{\sqrt{3}}$.Since $	an 	heta = \frac{1}{\sqrt{3}}$,we have $	heta = 30^\circ$.The acceleration of a block on a smooth inclined plane is $a = g \sin 	heta$.Thus,$a = 10 	imes \sin(30^\circ) = 10 	imes 0.5 = 5 \ m/s^2$.

Similar Questions

In the figure shown,$A$ and $B$ are free to move. All the surfaces are smooth. Then for $(0 < \theta < 90^o)$:

$A$ solid sphere,a hollow sphere,and a ring are released from the top of an inclined plane (frictionless) so that they slide down the plane. Then,the maximum acceleration down the plane is for (no rolling):

$A$ perfectly smooth sphere $A$ of mass $2 \ kg$ is in contact with a rectangular block $B$ of mass $4 \ kg$ and a vertical wall as shown in the figure. All surfaces are smooth. Find the normal reaction exerted by the vertical wall on sphere $A$ (in $N$). Take $g = 10 \ m/s^2$.

As shown in the figure,two spheres are released from point $A$ along paths $AB$ and $AC$ respectively. If both surfaces are smooth,find the time taken by both spheres to reach the bottom of the incline. (Take $g = 10 \, m/s^2$)

$A$ truck of mass $10,000\, kg$ moves up an inclined plane rising $1$ in $50$ with a speed of $36\, km/h$. Find the power of the engine in $kW$ $(g = 10\, m/s^2)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module