CBSE
A jar filled with two non-mixing liquids 1 and 2 having densities ρ_{1} and ρ_{2} respectively. A solid ball, made of a material of density ρ_{3}, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ_{1}, ρ_{2} and ρ_{3}?
ρ_{3} < ρ_{1} < ρ_{2}
ρ_{1} < ρ_{3} < ρ_{2}
ρ_{1} < ρ_{2} < ρ_{3}
ρ_{1} < ρ_{3} < ρ_{2}
D.
ρ_{1} < ρ_{3} < ρ_{2}
As liquid 1 floats above liquid 2,
ρ_{1} < ρ_{2}
The ball is unable to sink into liquid 2, ρ_{3} < ρ_{2}
The ball is unable to rise over liquid 1
ρ_{1} < ρ_{3} Thus, ρ_{1} < ρ_{3} < ρ_{2}
A spherical solid ball of volume V is made of a material of density ρ_{1}. It is falling through a liquid of density ρ_{2}(ρ_{2} <ρ_{1}). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv^{2} (k>0). The terminal speed of the ball is
A.
ρ_{1}Vg − ρ_{2}Vg = kv_{2}^{T}
The speed of sound in oxygen (O_{2}) 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}
650 ms^{−1}
A.
1420 ms^{−1}
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
36 > x > 18
B.
x >54
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 k_{1} = 3 and thickness d/3 while the other one has dielectric constant k_{2} = 6 and thickness 2d/3 . Capacitance of the capacitor is now
1.8 pF
45 pF
40.5 pF
20.25 pF
C.
40.5 pF
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 = 12.50 , β =π/ 2.0
A.
α = 25.00 π, β = π
y = 0.005 cos (αx − βt)
comparing the equation with the standard form,
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
55 Ω
B.
220 Ω
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
3.38 mm
D.
3.38 mm
Diameter = M.S.R. + C.S.R × L.C. + Z.E.
= 3 + 35 × (0.5/50) + 0.03
= 3.38 mm
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?
C.
Capillary rise h = 2T cosθ /ρgr. As soap solution has lower T, h will be low.
An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V_{1} and contains ideal gas at pressure P1 and temperature T_{1}. The other chamber has volume V_{2} and contains ideal gas at pressure P_{2} and temperature T_{2}. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
A.