A uniform cylinder of length L and mass M having cross-sectional area A is suspended with its length…..

Q: A uniform cylinder of length L and mass M having cross-sectional area A is suspended with its length vertical from a fixed point by a massless spring (Spring constant = k) such that it is half submerged in a liquid of density σ at equilibrium position. The extension x0 of the spring when it is in equilibrium, is

(a) \displaystyle \frac{Mg}{k}

(b) \displaystyle \frac{Mg}{k} (1- \frac{LA\sigma}{M})

(c) \displaystyle \frac{Mg}{k} (1- \frac{LA\sigma}{2M})

(d) \displaystyle \frac{Mg}{k} (1+ \frac{LA\sigma}{M})

Ans: (c)

Water is flowing continuously from a tap having an internal diameter 8×10-3 The water velocity as it leaves the tap is 0.4 ms-1…

  1. Water is flowing continuously from a tap having an internal diameter 8×10-3 The water velocity as it leaves the tap is 0.4 ms-1. The diameter of the water stream at a distance 2 × 10-1 m below the tap is close to

(a) 7.5 × 10-3 m

(b) 9.6 ×110-3 m

(c) 3.6 ×10-3 m

(d) 5.0 × 10-3 m

Ans: (c)

A sphere falls from rest into water from a height of 2m. The relative density of the sphere is 0.80. Find the depth…

Q: A sphere falls from rest into water from a height of 2m. The relative density of the sphere is 0.80. Find the depth to which ball will sink (in m)

(a) 8         

(b) 3

(c) 6

(d) 5

Ans: (a)

Figure shows a liquid flowing through a tube at the rate of 0.1 m³s-1. The tube is branched into two semicircular tubes….

Q: Figure shows a liquid flowing through a tube at the rate of 0.1 m³s-1. The tube is branched into two semicircular tubes of cross-sectional area A/3 (at P) and 2A/3 (at Q) . The velocity of liquid at Q is (Given, the cross-section of the main tube is A = 10-2m² and vP = 20m/s)

Numerical

(a) 5 ms-1

(b) 30 ms-1

(c) 35 ms-1

(d) 10 ms-1

Ans: (a)

A large tank is filled with water (density = 1000 kg m-3). A small hole is made at a depth 10m below water surface…..

Q: A large tank is filled with water (density = 1000 kg m-3). A small hole is made at a depth 10m below water surface. The range of water issuing out of the whole is R on the ground. Approximately, what extra pressure must be applied on the water surface, so that range becomes 2R? (Given, 1atm = 105 Pa and g = 10ms-2)

Numerical

(a) 9 atm

(b) 4 atm

(c) 5 atm

(d) 3 atm

Ans: (d)