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Que. Water from a tap emerges vertically downwards with an initial speed of 1 m s The cross-sectional area of the tap is 10 4 m2 Assuming pressure to be constant through out the stream of water and flow to be steady, the cross-sectional area 0.15 m below the tap is (a) 10-4 m2 (c) 0.5 x 10-4 m2 (b) 105 m2 (d) 0.2 x 10 4 m2

By equation of continuity, Alvi = A2V2 or V,- ! 2 1/ 2 10-4 ><! or A2 2 VI+2 10 0.15 +2gh = 0.5 10-4 m2

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant k. A mass m hangs freely from the free end of the spring. The area of cross-section and the Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to Que. m(YA + kL) YAk (a) 2 (b) 2 mYA N kL (d) 2rt, ml (c) 2 VYA

For two springs in series, the equivalent force constant is kea-2. Here, ki-k and k1 + k2 YA 2 kYA kYA k =-L- eg YA kL YA m(YA kL) V YAk .. . T=2

Que. The speed of light (c), acceleration due to gravity (g) and pressure (P) are taken as fundamental units, the dimensions of gravitational constant (G) are (a) Ic gP-3] (c) [cogP-] (b) c2gp-2] (d) c2gp-2]

Let G = kcxopz -1r 21z Equating both sides, we get, On solving, x = 0 y = 2, z =-1. Thus, [G] = [cog2P-1]

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