As shown in the above figure, two strings and a bob system of length l are maintained at an angle of 45° with the horizontal and the system is in equilibrium in the vertical plane. Now, if the bob is slightly displaced normal to the plane of the strings, find the time-period of oscillation T=?

Question

As shown in the above figure, two strings and a bob system of length l are maintained at an angle of 45° with the horizontal and the system is in equilibrium in the vertical plane. Now, if the bob is slightly displaced normal to the plane of the strings, find the time-period of oscillation T=? Question

(A) 2π √(2 √2 l/g) (B) 2π √(√2 l/g) (C) 2π √(l/g) (D) 2π √(l/√2 g)

Tardigrade Admin · Accepted Answer

The pendulum will oscillate in plane perpendicular to XY axis.
therefore, effective legth of oscillation is

l_{e ff ec t i v e}

=

\frac{l}{2}

and

g_{e ff ec t i v e} = g

T = 2 π \frac{l _{e ff ec t i v e}}{g _{e ff ec t i v e}}

T = 2 π \frac{l}{2 g}

$2 π \frac{2 2 l}{g}$

$2 π \frac{2 l}{g}$

$2 π \frac{l}{g}$

$2 π \frac{l}{2 g}$

The pendulum will oscillate in plane perpendicular to XY axis.
therefore, effective legth of oscillation is
$l_{e ff ec t i v e}$ = $\frac{l}{2}$ and $g_{e ff ec t i v e} = g$
$T = 2 π \frac{l _{e ff ec t i v e}}{g _{e ff ec t i v e}}$
$T = 2 π \frac{l}{2 g}$

Q. As shown in the above figure, two strings and a bob system of length l are maintained at an angle of 45∘ with the horizontal and the system is in equilibrium in the vertical plane. Now, if the bob is slightly displaced normal to the plane of the strings, find the time-period of oscillation T=?

2πg22l​​​

2πg2l​​​

2πgl​​

2π2​gl​​

The pendulum will oscillate in plane perpendicular to XY axis. therefore, effective legth of oscillation is leffective​ = 2​l​ and geffective​=g T=2πgeffective​leffective​​​ T=2π2​gl​​​

$2 π \frac{2 2 l}{g}$

$2 π \frac{2 l}{g}$

$2 π \frac{l}{g}$

$2 π \frac{l}{2 g}$

The pendulum will oscillate in plane perpendicular to XY axis.
therefore, effective legth of oscillation is
$l_{e ff ec t i v e}$ = $\frac{l}{2}$ and $g_{e ff ec t i v e} = g$
$T = 2 π \frac{l _{e ff ec t i v e}}{g _{e ff ec t i v e}}$
$T = 2 π \frac{l}{2 g}$