A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12 . Keeping the box in stationary state over the trolley, the maximum acceleration with which the trolley can be moved horizontally in $\mathrm{m} \mathrm{s}^{-2}$ is:
$$ \left(g=10 \mathrm{~m} / \mathrm{s}^2\right) $$
2.1
1.8
1.5
1.2
Five capacitors of capacitances
$C_1=C_2=C_3=C_4=10 \mu \mathrm{~F}$ and $C_5=2.5 \mu \mathrm{~F}$ are connected as shown, along with a battery of 50 V .
The equivalent capacitance and the charges on each capacitor respectively are:
$5 \mu \mathrm{~F}, 125 \mu \mathrm{C}$ on $C_1$ to $C_4$ and $25 \mu \mathrm{C}$ on $C_5$
$5 \mu \mathrm{~F}, 125 \mu \mathrm{C}$ on all capacitors
$5 \mu \mathrm{~F}, 250 \mu \mathrm{C}$ on all capacitors
$4 \mu \mathrm{~F}, 250 \mu \mathrm{C}$ on $C_1$ to $C_4$ and $125 \mu \mathrm{C}$ on $C_5$
The amount of work done to raise a mass ' $m$ ' from the surface of the Earth to a height equal to the radius of the Earth ' $R$ ' will be
$2 m g R$
$m g \frac{R}{4}$
$m g R$
$m g \frac{R}{2}$
Each side of a metallic cube of mass 5.580 kg is measured to the 9.0 cm . Keeping the significant figures in view, the density of the material of the cube can be best expressed as $X \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ where the value of $X$ is:
7.654
7.6
7.65
7.7
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