A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is T. When the sphere is immersed in a non-viscous liquid of density 1/10 that of brass, it will act as a simple pendulum of period :

Question

A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is T. When the sphere is immersed in a non-viscous liquid of density 1/10 that of brass, it will act as a simple pendulum of period : (A)  T  (B)  (10/9)T  (C)  √( (9/10) )T  (D)  √( (10/9) )T

Tardigrade Admin · Accepted Answer

The time period pendulum in air T=2 π √(l/g)..(i) l being the length of simple pendulum. In liquid, effective weight of sphere w prime= weight of bob in air - up thrust ⇒ ρ v gf f=m g-m prime g =ρ v g=ρ prime v g=(ρ-ρ prime) v g where ρ prime= density of sphere ρ= density of liquid ∴ g text eff =((ρ-ρ / 10/ρ)) g=(9/10) g Thus, T prime=2 π √(l/g text eff ) =2 π √(l/(9)10 g) (T prime/T)=√(10/9) or T prime=√(10/9) T

Q. A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is $T$ . When the sphere is immersed in a non-viscous liquid of density $1/10$ that of brass, it will act as a simple pendulum of period :

$T$

$\frac{10}{9} T$

$(\frac{9}{10}) T$

$(\frac{10}{9}) T$

Q. A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is T. When the sphere is immersed in a non-viscous liquid of density 1/10 that of brass, it will act as a simple pendulum of period :

T

910​T

(109​)​T

(910​)​T

Q. A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is $T$ . When the sphere is immersed in a non-viscous liquid of density $1/10$ that of brass, it will act as a simple pendulum of period :

$T$

$\frac{10}{9} T$

$(\frac{9}{10}) T$

$(\frac{10}{9}) T$