A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be

Question

A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be (A) 2 π √(((R-r) 1.4/g)) (B) 2 π √((R-r/g)) (C) 2 π √((r R/a)) (D) 2 π √((R/g r))

Tardigrade Admin · Accepted Answer

Tangential acceleration, ai=-g sin θ=-g θ at=-g (x/(R-r)) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e884d7ebe3a233f5beb7a54b038aae7a-.png" /> Motion is S.H.M., with time period T=2 π √( text displacement / text acceleration ) =2 π √(x/(g x)(R-r)) =2 π √(R-r/g)

$2 π (\frac{( R - r ) 1.4}{g})$

$2 π (\frac{R - r}{g})$

$2 π (\frac{r R}{a})$

$2 π (\frac{R}{g r})$

Tangential acceleration, $a_{i} = - g sin θ = - g θ$
$a_{t} = - g \frac{x}{( R - r )}$

Motion is S.H.M., with time period
$T = 2 π \frac{displacement}{acceleration}$
$= 2 π \frac{x}{\frac{gx}{( R - r )}}$
$= 2 π \frac{R - r}{g}$

2π(g(R−r)1.4​)​

2π(gR−r​)​

2π(arR​)​

2π(grR​)​

Tangential acceleration, ai​=−gsinθ=−gθ at​=−g(R−r)x​ Motion is S.H.M., with time period T=2π acceleration displacement ​​ =2π(R−r)gx​x​​ =2πgR−r​​

$2 π (\frac{( R - r ) 1.4}{g})$

$2 π (\frac{R - r}{g})$

$2 π (\frac{r R}{a})$

$2 π (\frac{R}{g r})$

Tangential acceleration, $a_{i} = - g sin θ = - g θ$
$a_{t} = - g \frac{x}{( R - r )}$

Motion is S.H.M., with time period
$T = 2 π \frac{displacement}{acceleration}$
$= 2 π \frac{x}{\frac{gx}{( R - r )}}$
$= 2 π \frac{R - r}{g}$