A test tube with some lead shots in it has a total mass M. It floats upright in a liquid of density d. The crosssectional area of the tube is A. It is pressed slightly downwards from position of stable equilibrium and released. It executes SHM with a period of

Question

A test tube with some lead shots in it has a total mass M. It floats upright in a liquid of density d. The crosssectional area of the tube is A. It is pressed slightly downwards from position of stable equilibrium and released. It executes SHM with a period of (A) 2 π √(M/A g d) (B) 2 π √(M/2 A g d) (C) 2 π √(2 M/A g d) (D) 2 π √(M A/g d)

Tardigrade Admin · Accepted Answer

F=-(A x) d g or F=-(A d g) x ⇒ k=A d g ⇒ T=2 π √(m/k)=2 π √(M/A g d)

Q. A test tube with some lead shots in it has a total mass $M$ . It floats upright in a liquid of density $d$ . The crosssectional area of the tube is $A$ . It is pressed slightly downwards from position of stable equilibrium and released. It executes SHM with a period of

$2 π \frac{M}{A g d}$

$2 π \frac{M}{2 A g d}$

$2 π \frac{2 M}{A g d}$

$2 π \frac{M A}{g d}$

$F = - (A x) d g$
or $F = - (A d g) x$
$\Rightarrow k = A d g$
$\Rightarrow T = 2 π \frac{m}{k} = 2 π \frac{M}{A g d}$

Q. A test tube with some lead shots in it has a total mass M. It floats upright in a liquid of density d. The crosssectional area of the tube is A. It is pressed slightly downwards from position of stable equilibrium and released. It executes SHM with a period of

2πAgdM​​

2π2AgdM​​

2πAgd2M​​

2πgdMA​​