Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

• 3.32 mm 

• 3.73 mm

• 3.67 mm

• 3.67 mm

A spherical solid ball of volume V is made of a material of density ρ₁. It is falling through a liquid of density ρ₂(ρ₂ <ρ₁). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv² (k>0). The terminal speed of the ball is

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance.Then 

• 18 > x

• x >54

• 54 > x > 36 

• 54 > x > 36 

The speed of sound in oxygen (O₂) at a certain temperature is 460 ms⁻¹. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

• 1420 ms⁻¹

• 550 ms⁻¹

• 375 ms⁻¹

• 375 ms⁻¹

A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ₁, ρ₂ and ρ₃?

• ρ₃ < ρ₁ < ρ₂

• ρ₁ < ρ₃ < ρ₂

• ρ₁ < ρ₂ < ρ₃

• ρ₁ < ρ₂ < ρ₃

16.

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution.Which of the following shows the relative nature of the liquid columns in the two tubes? 

• 
• 
• 
• 

A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos (αx −βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are 

• α = 25.00 π, β = π

• α = 0.08/ π,  2.0/π

• α = 0.04 / π , β =1.0/π

• α = 0.04 / π , β =1.0/π

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V₁ and contains ideal gas at pressure P1 and temperature T₁. The other chamber has volume V₂ and contains ideal gas at pressure P₂ and temperature T₂. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.

The value of the unknown resistor R is

• 13.75 Ω

• 220 Ω

• 110 Ω

• 110 Ω

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k₁ = 3 and thickness d/3 while the other one has dielectric constant k₂ = 6 and thickness 2d/3 . Capacitance of the capacitor is now 

• 1.8 pF 

• 45 pF

• 40.5 pF

• 40.5 pF