A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0oC such that its height above the water surface is 20cm. When the temperature of water is increased to 4oC, the height of the cylinder above the water surface becomes 21cm. The density of water at T=4oC, relative to the density at T=0oC is close to:
Held on 8 Jan 2020 · Verified 6 Jul 2026.
1.26
1.04
1.01
1.03
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Net gravitational force at the center of a square is found to be $F_{1}$ when four particles having mass $M, 2 M, 3 M$ and $4 M$ are placed at the four corners of the square as shown in figure and it is $F_{2}$ when the positions of $3 M$ and $4 M$ are interchanged. The ratio $\frac{F_{1}}{F_{2}}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is $\_\_\_\_$. 
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The surface tension of a soap solution is $3.5 \times 10^{-2}$ N/m. The work required to increase the radius of a soap bubble from $1$ cm to $2$ cm is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _____. ($\pi = 22/7$)
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