A balloon is moving up in air vertically above a point A on the ground. When it is at a height h₁, a girl standing at a distanced (point B) from A (see figure) sees it at an angle 45^o with respect to the vertical. When the balloon climbs up a further height h₂, it is seen at an angle 60^o with respect to the vertical if the girl moves further by a distance 2.464 d(point C). Then the height h₂ is (given tan 30^o = 0.5774)

A galvanometer of resistance G is converted into a voltmeter of range 0 – 1 V by connecting a resistance R₁ in series with it. The additional resistance that should be connected in series with R₁ to increase the range of the voltmeter to 0 – 2 V will be :

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is :

The value of the acceleration due to gravity is g₁ at a height h = $${R \over 2}$$ (R = radius of the earth) from the surface of the earth. It is again equal to g₁ at a depth d below the surface of the earth. The ratio $$\left( {{d \over R}} \right)$$ equals :