A frictionless wire A B is fixed on a sphere of radius R. A very small spherical ball slips on this wire the time taken by this ball to slip from A to B is

Question

A frictionless wire A B is fixed on a sphere of radius R. A very small spherical ball slips on this wire the time taken by this ball to slip from A to B is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6e6dad993135f4256d951a8fae5d97fb-.png" /> (A) (2 √g R/g cos θ) (B) 2 √g R ( cos θ/g) (C) 2 √(R/g) (D) (g R/√g cos θ)

Tardigrade Admin · Accepted Answer

Acceleration of body along A B is g cos θ Distance travelled in time t sec =A B=(1/2)(g cos θ) t2 From Δ A B C, A B=2 R cos θ 2 R cos θ =(1/2) g cos θ t2 t2 =(4 R/g) t =2 √(R/g)

Q. A frictionless wire $A B$ is fixed on a sphere of radius $R$ . A very small spherical ball slips on this wire the time taken by this ball to slip from $A$ to $B$ is

$\frac{2 g R}{g c o s θ}$

$2 g R \frac{c o s θ}{g}$

$2 \frac{R}{g}$

$\frac{g R}{g c o s θ}$

Acceleration of body along $A B$ is $g cos θ$
Distance travelled in time $t sec = A B = \frac{1}{2} (g cos θ) t^{2}$
From $Δ A BC, A B = 2 R cos θ$
$2 R cos θ = \frac{1}{2} g cos θ t^{2}$
$t^{2} = \frac{4 R}{g}$
$t = 2 \frac{R}{g}$

Q. A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire the time taken by this ball to slip from A to B is

gcosθ2gR​​

2gR​gcosθ​

2gR​​

gcosθ​gR​