Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m². It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 m/s²)

Option 1 -

3 m/s

Option 2 -

5 m/s

Option 3 -

2 m/s

Option 4 -

4 m/s

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A calorimeter of water equivalent $20 g$ contains $180 g$ of water at $25^{?} C$ , ' $m$ ' grams of steam at $100^{?} C$ is mixed in it till the temperature of the mixture is $31^{?} C$ . The value of

alok kumar singh

Heat lost by steam $=$ Heat gained by water and calorimeter.

$\begin{array}{r} m \times 540 + m \times 1 \times (100 - 31) = 200 \\ 540 m + 69 m = 1200 \\ m = \frac{1200}{609} \approx 2 \end{array}$

Match List I with List II.

List I List II

(a) Isothermal (i) Pressure constant

(b) Isochoric (ii) Temperature constant

(c) Adiabatic (iii) Volume constant

(d) Isobaric (iv) Heat content is constant

Choose the correct answer from the options given below:

alok kumar singh

In isothermal process, temperature is constant.

In isochoric process, volume is constant.

In adiabatic process, there is no exchange of heat.

In isobaric process, pressure is constant

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Choose the incorrect option from the following:

alok kumar singh

N_a -> Avogadro’s Number

$J β^{2} \equiv [μ k R] \Rightarrow β^{2} \equiv [k R] \Rightarrow β \equiv [k] \equiv [M L^{2} T^{- 2} K^{- 1}]$

, and

-> $S \equiv α^{2} β \Rightarrow [M L^{2} T^{- 2} K^{- 1}] \equiv α^{2} [M L^{2} T^{- 2} K^{- 1}] \Rightarrow α \equiv [M^{0} L^{2} T^{0} K^{0}]$ Dimensionless

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alok kumar singh

Heat absorbed in cyclic process = Work done = 100? Joule

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alok kumar singh

Since process is isochoric, so

$Q = n C_{v} Δ T = n (\frac{f}{2} R) Δ T = 4 (\frac{5}{2} \times R) (50) = 500 R$