A ball whose size is slightly smaller than th | vedclass

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

Question

(B) The velocity at the bottommost point is $v_0 = 10 \, m/s$. The radius is $R = 2.5 \, m$. The critical velocity required to complete the vertical c

Vedclass · Accepted Answer

$N_1 > 0$ for motion in $CDA$,$N_2 > 0$ for motion in $ABC$

Vedclass · Answer

(B) The velocity at the bottommost point is $v_0 = 10 \, m/s$. The radius is $R = 2.5 \, m$. The critical velocity required to complete the vertical circle is $v_c = \sqrt{5gR} = \sqrt{5 	imes 10 	imes 2.5} = \sqrt{125} \approx 11.18 \, m/s$. Since $v_0 At any angle $	heta$ from the bottom,the radial equation is $N - mg \cos 	heta = \frac{mv^2}{R}$,where $N$ is the normal force. By conservation of energy,$\frac{1}{2}mv_0^2 = \frac{1}{2}mv^2 + mgR(1 - \cos 	heta)$,so $v^2 = v_0^2 - 2gR(1 - \cos 	heta) = 100 - 50(1 - \cos 	heta) = 50 + 50 \cos 	heta$.Substituting $v^2$ into the radial equation: $N = mg \cos 	heta + \frac{m}{R}(50 + 50 \cos 	heta) = mg \cos 	heta + 20mg + 20mg \cos 	heta = mg(20 + 21 \cos 	heta)$.For the bottom half (where $\cos 	heta > 0$),$N > 0$,meaning the ball presses against the outer wall $(N_2)$.For the top half (where $\cos 	heta Thus,$N_2 > 0$ for the lower part $(ABC)$ and $N_1 > 0$ for the upper part $(CDA)$.

Similar Questions

$A$ body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $AB = D$. The height $h$ is equal to

$A$ ball of mass $2 \,g$ released from the top of an inclined plane describes a circular motion of radius $20 \,cm$ in the vertical plane upon reaching the bottom. The minimum height of the inclined plane is (in $\,cm$)

$A$ weightless thread can support a tension of up to $30 \, N$. $A$ stone of mass $0.5 \, kg$ is tied to it and is revolved in a circular path of radius $2 \, m$ in a vertical plane. If $g = 10 \, m/s^2$,then the maximum angular velocity of the stone will be ........ $rad/s$.

The bob of a simple pendulum is of mass $10 \, g$. It is suspended with a thread of $1 \, m$. If we hold the bob so as to stretch the string horizontally and release it,what will be the tension at the lowest position? (Take $g = 10 \, m/s^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module