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

• $\frac{\mathrm{YxA}}{2\mathrm{L}}$

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

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

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

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

25.

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