MCQ
Standing waves are generated on a sonometer string loaded with a cylindrical body. If the cylinder is completely immersed in water, the length of the loops changes by a factor of $2.2$ . The specific gravity of the material of the cylinder is 
  • A
    $1.11$
  • B
    $2.15$
  • C
    $2.50$
  • $1.26$

Answer

Correct option: D.
$1.26$
d
$f=\frac{V}{\lambda_{1}}=\frac{1}{\lambda_{1}} \sqrt{\frac{T_{1}}{\mu}}$

$\mathrm{f}=\frac{\mathrm{V}}{\lambda_{1}}=\frac{1}{\lambda_{1}} \sqrt{\frac{\mathrm{T}_{2}}{\mu}}$

$\frac{1}{\lambda_{1}} \sqrt{\frac{T_{1}}{\mu}}=\frac{1}{\lambda_{2}} \sqrt{\frac{T_{2}}{\mu}}$

$\sqrt{\frac{\mathrm{T}_{1}}{\mu}}=\left(\frac{\lambda_{1}}{\lambda_{2}}\right) \sqrt{\frac{\mathrm{T}_{2}}{\mu}}$

$\mathrm{T}_{1}=(2.2)^{2} \cdot \mathrm{T}_{2}$

$\mathrm{Mg}=4.84\left[\mathrm{Mg}-\frac{\mathrm{M}}{(\mathrm{S} \cdot \mathrm{G})} \cdot \mathrm{g}\right]$

$1=4.84-\frac{4.84}{\mathrm{S.G}}$

$\frac{4.84}{\mathrm{S.G}}=3.84 \Rightarrow \mathrm{S.G}=\frac{4.84}{3.84}$

$\Rightarrow \mathrm{S.G}=1.26$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A wire of $1 \,\Omega$ has a length of $1\, m$. It is stetched till its length increases by $25\, \%$. The percentage change in resistance to the neartest integer is .....$\%$
A particle of mass $m$ moves in a circular path of radius $r$, under the action of force which delivers it constant power $p$ and increases its speed. The angular acceleration of particle at time $(t)$ is proportional
The half life period of radium is $1600$ years. The fraction of a sample of radium that would remain after $6400$ years is
As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius a and outer radius $b$. The electric field due to charge $Q$ in three different regions I, II and III is given by: $( I : r < a , II : a < r < b , III : r > b )$
Which of the following cannot be emitted by radioactive substances during their decay
Consider the efficiency of Carnot's engine is given by $\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}$, where $\alpha$ and $\beta$ are constants. If $T$ is temperature, $k$ is Boltzman constant, $\theta$ is angular displacement and $x$ has the dimensions of length. Then, choose the incorrect option.
Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 K$ . The piston of $A$ is free to move while that of $B$  is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30 K$ , then the rise in temperature of the gas in $B$ is ..... $K$
The force of gravitation is
A semiconductor device is connected in a series circuit with a battery and a resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops almost to zero. The device may be
A solid sphere is thrown up a rough incline. The sphere rolls up without slipping and eventually comes down rolling without slipping. The direction of rolling friction in upward and downward motion respectively is ............