1
JEE Advanced 2020 Paper 2 Offline
Numerical
+3
-1
A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of the density of air with height h from the ground is
$$\rho \left( h \right) = {\rho _0}{e^{ - {h \over {{h_0}}}}}$$, where $$\rho$$0 = 1.25 kg m−3 and h0 = 6000 m, the value of N is _________.
2
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
A cubical solid aluminium (bulk modulus = $$- V{{dP} \over {dV}} = 70GPa$$) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 103 kg m-3 and 10 ms-2, respectively, the change in the edge length of the block in mm is _______.
3
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration
due to gravity are 103 kg m−3 , 0.07 Nm−1 and 10 ms−2 , respectively, the value of h (in mm) is _________.
4
JEE Advanced 2019 Paper 1 Offline
Numerical
+3
-0
A block of weight 100 N is suspended by copper and steel wires of same cross-sectional area 0.5 cm2 and length $$\sqrt 3$$ m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30$$^\circ$$ and 60$$^\circ$$, respectively. If elongation in copper wire is ($$\Delta {l_c}$$) and elongation in steel wire is ($$\Delta {l_s}$$), then the ratio $${{\Delta {l_c}} \over {\Delta {l_s}}}$$ is .............. .

[Young's modulus for copper and steel are 1 $$\times$$ 1011 N/m2 and 2 $$\times$$ 1011 N/m2 respectively.]