The period of vibration of a mass m suspended from a spring is 2 s. If along with it  another mass of 2 kg is also suspended, the period of oscillation increases by ls. The mass m will be

• 2 kg

• 1 kg

• 1.6 kg

• 2.6 kg

A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. It is stretched by an amount x. The work done is

• $\frac{\mathrm{YxA}}{2\mathrm{L}}$

• $\frac{{\mathrm{Yx}}^2\mathrm{A}}{\mathrm{L}}$

• $\frac{{\mathrm{Yx}}^2\mathrm{A}}{2\mathrm{L}}$

• $\frac{2{\mathrm{Yx}}^2\mathrm{A}}{\mathrm{L}}$

23.

Compressibility of water is 5 x 10^-10 m² /N. The change in volume of 100 mL water subjected to 15 x 10⁶ Pa pressure will

• no change

• increase by 0.98 mL

• decrease by 0.75 mL

• increase by 1.50 mL

The force of cohesion is

• maximum in solids

• maximum in liquids

• maximum in gases

• same in solid, liquid and gas

The temperature at which root mean square velocity of molecules of helium is equal to root mean square velocity of hydrogen at NTP is

• 273°C

• 273 K

• 546°C

• 844 K

For adiabatic process  $\left(\mathrm{\gamma } = \frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{V}}}\right)$

• ${\mathrm{p}}^{\mathrm{\gamma }}\mathrm{V} = \mathrm{constant}$

• ${\mathrm{Tp}}^{\mathrm{\gamma }}\mathrm{V} = \mathrm{constant}$

• ${\mathrm{pV}}^{\mathrm{\gamma }} = \mathrm{constant}$

• pV = constant

A cup of tea having the temperature 80°C is kept in a room,which is at 20°C. Which of the given curves best represents the variation of temperature T of the cup with time t ?

An ice box made of Styrofoam (thermal conductivity = 0.01 Jm^-1s^-1K) is used to keep liquids cool. It has a total wall area including lid of 0.8 m² and wall thickness of 2.0 cm. A bottle of water is placed in the box and filled with ice. If the outside temperature is 30°C, the rate of flow of, heat into the box is (in Js^-1)

• 16

• 14

• 12

• 10

The length of two open organ pipes are l and (l+ Δl) respectively. Neglecting end corrections the beats frequency between them will be approximately

• $\frac{\mathrm{v}}{2\mathrm{l}}$

• $\frac{\mathrm{v}}{4\mathrm{l}}$

• $\frac{\mathrm{v}∆\mathrm{l}}{2{\mathrm{l}}^2}$

• $\frac{\mathrm{v}∆\mathrm{l}}{\mathrm{l}}$

5 g of ice of O°C is dropped in a beaker containing 20 g of water at 40°C. The final temperature will be

• 32°C

• 16°C

• 8°C

• 24°C