A small body of mass m slides down from the t | vedclass

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

Question

(B) Let the body lose contact at an angle $	heta$ with the vertical. At this point,the normal force $N$ becomes zero.The radial forces acting on the

Vedclass · Accepted Answer

$\frac{2}{3}r$

Vedclass · Answer

(B) Let the body lose contact at an angle $	heta$ with the vertical. At this point,the normal force $N$ becomes zero.The radial forces acting on the body are the component of gravity $mg \cos 	heta$ and the normal force $N$. The centripetal force is provided by the radial component of gravity:$mg \cos 	heta - N = \frac{mv^2}{r}$Since $N = 0$ at the point of losing contact,we have:$mg \cos 	heta = \frac{mv^2}{r} \implies v^2 = rg \cos 	heta$Using the principle of conservation of mechanical energy between the top of the hemisphere and the point where it loses contact:$mg r = mg(r \cos 	heta) + \frac{1}{2}mv^2$$gr = gr \cos 	heta + \frac{1}{2}v^2$Substitute $v^2 = rg \cos 	heta$ into the energy equation:$gr = gr \cos 	heta + \frac{1}{2}(rg \cos 	heta)$$gr = gr \cos 	heta + \frac{1}{2}gr \cos 	heta$$1 = \cos 	heta + \frac{1}{2} \cos 	heta = \frac{3}{2} \cos 	heta$$\cos 	heta = \frac{2}{3}$The height $h$ from the base is given by $h = r \cos 	heta$.Therefore,$h = r \left(\frac{2}{3}ight) = \frac{2}{3}r$.

$A$ small body of mass $m$ slides down from the top of a hemisphere of radius $r$. The surfaces of the block and the hemisphere are frictionless. The height at which the body loses contact with the surface of the sphere is

Similar Questions

The period of the function $f(\theta) = \sin \frac{\theta}{3} + \cos \frac{\theta}{2}$ is (in $pi$)

The refractive index of the material of the prism for violet colour is $1.69$ and that for red is $1.65$. If the refractive index for mean colour is $1.66$,what is the dispersive power of the material of the prism?

Which of the following hydroxides is acidic?

What are the oxidation states of iron and chromium in chromite ore,respectively?

If the mean of a Poisson distribution is $\frac{1}{2}$,then the ratio of $P(X=3)$ to $P(X=2)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module