Class 11th

The main mechanical properties of fluids are exerting pressure, resisting flow or viscosity, forming surface tension, following Bernoulli's principle, and moving in a streamline.

If $P_1=P$ then $P_2=P+5\%$ of $P=1.05P.$

From Boyle's law, $PV=constant$ therefore,

$\frac{V_2}{V_1}=\frac{P_1}{P_2}=\frac{P}{1.05P}=\frac{100}{105}$

Fractional change in volume is

$\frac{\Delta V}{V}=\frac{V_2-V_1}{V_1}=\frac{100-105}{105}=-\frac{5}{105}$

Therefore, percentage change in volume is

$\frac{\Delta V}{V}*100\%=-\frac{5}{105}*100\%=-4.76\%$

That is, volume decreases by $4.76\mathrm{\%}.$

From first law of thermodynamics

$?W=?Q-?U$

$?Q=n{C}_p?T$

$?U=n{C}_v?T$

$?W=n(C_p-C_v)?T$

$\frac{?Q}{?W}=\frac{\gamma }{\gamma -1}\left. [\frac{C_p}{C_p}=\gamma \right]$

From F.B. Ds of

$9kg\to 90-T_1=9a\dots .\left(1\right)$

$6kg\to T_1-T_2=6a\dots ..\left(2\right)$

$5kg\to T_2-50=5a\dots ..\left(3\right)$

$\left(1\right)+\left(2\right)+\left(3\right)$

$40=20a?a=2m/s^2$

Bulk modulus

$B=\frac{-\Delta P}{\Delta V/V}$

$B=-V\left[\frac{\Delta P}{\Delta V}\right]$

$B=-V\left[\frac{\partial P}{\partial V}\right]$

^{$B=-V\left[\frac{\partial P}{\partial V}\right]$}

$B=-V\left[\frac{-P}{V}\right]$

$\Rightarrow B=P$

m  =l0 kg

h= 5m

By work energy theorem

$mgh=\frac{1}{2}m{v}^2$

$v^2=2$ gh 

$v=\sqrt[]{2gh}$

$v=\sqrt[]{100}$

$v=10m/s$

In a number without decimal, trailing zeros are insignificant. If a number has a decimal, then preceding zeros are insignificant.

Hence, in 40.40 all zeros are significant

$kx=mg-F_{up}$

$kx=mg-\frac{md}{D}g$

$x=\frac{mg}{k}\left(1-\frac{d}{D}\right)$