A smooth sphere of radius R moves along a str | vedclass

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

Question

(D) The sphere moves with acceleration $a = g$ towards the left,so the particle experiences a pseudo force $F_p = ma = mg$ towards the right.Let the p

Vedclass · Accepted Answer

$\sqrt{2Rg(1 + \sin 	heta - \cos 	heta)}$

Vedclass · Answer

(D) The sphere moves with acceleration $a = g$ towards the left,so the particle experiences a pseudo force $F_p = ma = mg$ towards the right.Let the particle be at the top of the sphere at $t = 0$. As it slides to an angle $	heta$ from the vertical,the vertical displacement is $h = R(1 - \cos 	heta)$ and the horizontal displacement is $d = R \sin 	heta$.Applying the work-energy theorem relative to the sphere:$W_g + W_{pseudo} = \Delta K.E.$Work done by gravity: $W_g = mg \cdot h = mgR(1 - \cos 	heta)$.Work done by pseudo force: $W_{pseudo} = F_p \cdot d = (mg)(R \sin 	heta)$.Since the initial kinetic energy is zero,the final kinetic energy is $\frac{1}{2}mv^2$:$mgR(1 - \cos 	heta) + mgR \sin 	heta = \frac{1}{2}mv^2$.Dividing by $m$ and multiplying by $2$:$2gR(1 - \cos 	heta + \sin 	heta) = v^2$.Therefore,$v = \sqrt{2gR(1 + \sin 	heta - \cos 	heta)}$.

Similar Questions

$A$ body of mass $1.0 \, kg$ is falling with an acceleration of $10 \, m/s^2$. Its apparent weight will be ......... $kg \, wt$ $(g = 10 \, m/s^2)$.

$A$ vessel containing water is given a constant acceleration $a$ towards the right,along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?

$A$ car is moving on a circular horizontal track of radius $10 \, m$ with a constant speed of $10 \, m/s$. $A$ plumb bob is suspended from the roof of the car by a light rigid rod of length $1.00 \, m$. The angle made by the rod with the vertical is ........ $^o$.

$A$ smooth rod of length $l$ is kept inside a trolley at an angle $\theta$ as shown in the figure. What should be the acceleration $a$ of the trolley so that the rod remains in equilibrium with respect to it?

Vedclass Test Series

Exam Paper Generator

Online Exam Module