
- A$a_1=a_2$
- ✓$a_1=2 a_2$
- C$2 a_1=a_2$
- D$a_1=4 a_2$

For $8 kg T^{\prime}=8 a_1 \ldots(i)$
for $4 kg$
$4 g-T=4 a_2 \ldots(ii)$
for pulley
$T^1=2 T \ldots(iii)$
Using $(i), (ii)$ and $(iii)$
$a_2=\frac{a_1}{2}$
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$1.$ If the piston is pushed at a speed of $5 \ mms ^{-1}$, the air comes out of the nozzle with a speed of
$(A)$ $0.1 \ ms ^{-1}$ $(B)$ $1 \ ms ^{-1}$ $(C)$ $2 \ ms ^{-1}$ $(D)$ $8 \ ms ^{-1}$
$2.$ If the density of air is $\rho_{ a }$ and that of the liquid $\rho_{\ell}$, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to
$(A)$ $\sqrt{\frac{\rho_{ a }}{\rho_{\ell}}}$ $(B)$ $\sqrt{\rho_a \rho_{\ell}}$ $(C)$ $\sqrt{\frac{\rho_{\ell}}{\rho_{ a }}}$ $(D)$ $\rho_{\ell}$
Give the answer question $1$ and $2.$