A bead P slides on a frictionless semi-circul | vedclass

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

Question

(B) Let the radius of the semi-circle be $R$. The horizontal distance covered by bead $Q$ to reach point $B$ is $2R$. Since it moves with a constant h

Vedclass · Accepted Answer

$t_{P} < t_{Q}$

Vedclass · Answer

(B) Let the radius of the semi-circle be $R$. The horizontal distance covered by bead $Q$ to reach point $B$ is $2R$. Since it moves with a constant horizontal velocity $v$, the time taken is $t_Q = \frac{2R}{v}$.For bead $P$, the horizontal component of velocity is given as $v_x = v$ at point $S$. As the bead slides down the frictionless semi-circular wire, its speed increases due to gravity. The horizontal component of its velocity $v_x$ will be $v \cos 	heta$, where $	heta$ is the angle the velocity vector makes with the horizontal. Since the bead is constrained to move along the semi-circle, its horizontal velocity component $v_x$ will always be greater than or equal to its initial horizontal velocity $v$ as it moves towards $C$ and then towards $B$. Because the average horizontal velocity of $P$ is greater than $v$, and the total horizontal distance $P$ needs to cover is $2R$, the time taken $t_P$ must be less than $t_Q$.

Similar Questions

$A$ ball is moving to and fro about the lowest point $A$ of a smooth hemispherical bowl. If it is able to rise up to a height of $20 \,cm$ on either side of $A$,its speed at $A$ must be .......... $m/s$ (Take $g = 10 \,m/s^2$,mass of the body = $5 \,g$).

$A$ body of mass $m$ is travelling with a velocity $u$. When a constant retarding force $F$ is applied,it comes to rest after travelling a distance $s_{1}$. If the initial velocity is $2u$,with the same force $F$,the distance travelled before it comes to rest is $s_{2}$. Then,

Three different objects of masses $m_1, m_2$ and $m_3$ are allowed to fall from rest and from the same point $O$ along three different frictionless paths. The speeds of the three objects,on reaching the ground,will be in the ratio of

$A$ body falls freely under gravity. Its speed is $v$ when it has lost an amount $U$ of the gravitational potential energy. Then its mass is

$A$ car travelling at $80 \ km/h$ can be stopped at a distance of $60 \ m$ by applying brakes. If the same car travels at $160 \ km/h$ and the same braking force is applied,the stopping distance is: (in $m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module