Physics Test 249

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Physics Test 249

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Weekly Quiz Competition

Question 1
4 / -1

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P₂ be the pressure inside the inner bubble and P₀ be the pressure outside the outer bubble. Radius of another bubble with pressure difference P₂ - P₀ between its inside and outside would be

A
2.4 cm

B
12 cm

C
4.8 cm

D
6 cm

Solution
Question 2
4 / -1

A planet of mass M is revolving around sun in an elliptical orbit. If dA is the area swept in a time dt, angular momentum can be expressed as

A

B

C

D

Solution
Question 3
4 / -1

A spherical hole is made in a solid sphere of radius R. The mass of the original sphere was M.The gravitational field at the centre of the hole due to the remaining mass is

A
zero

B
GM/8R²

C
GM/2R²

D
GM/R²

Solution
Question 4
4 / -1

Directions For Questions

A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered wooden cylindrical block of diameter 4r, height h and density ρ/3.

Situation I : Initially, the tank is filled with water of density ρ to a height such that the height of water above the top of the block is h₁ (measured from the top of the block).

Situation II : The water is removed from the tank to a height h₂ (measured from the bottom of the block), as shown in the figure.

The height h₂ is smaller than h (height of the block) and thus the block is exposed to the atmosphere.

...view full instructions

Find the minimum value of height h₁ (in situation 1), for which the block just starts to move up?

A
2h/3

B
5h/4

C
5h/3

D
5h/2

Solution

Consider the equilibrium of wooden block.

Forces acting in the downward direction are

(b) Force due to pressure (P₁) created by liquid of height h₁ above the wooden block is

= P₁ × π (2r)² = [P₀ + h₁rg] × π (2r)²

Force acting on the upward direction due to pressure P₂ exerted from below the wooden block and atmospheric pressure is
Question 5
4 / -1

If the elastic limit of copper is 1.5 × 10⁸ N/ m², determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.

A
1.012 mm

B
0.912 mm

C
0.712 mm

D
0.812 mm

Solution
Question 6
4 / -1

At what temperature is the r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?

A
80 K

B
–73 K

C
3 K

D
20 K.

Solution
Question 7
4 / -1

Heat generated through a resistive wire will increase _______ times in unit time, if current in the wire becomes twice.

A
2

B
4

C
0.5

D
None of the above

Solution

So heat is given by

H = I² Rt

time is fixed, unit time, Resistance of wire will remain the same.

H ∝ I², factor = 4.

So,

H = k I² ---(1)

if the current becomes twice'

H' = k (2I)² ---(2)

(2) divided by (1) we get

So, H' : H = 4 : 1

So we see, the heat generated in unit time becomes 4 times of its initial value.
Question 8
4 / -1

The frequency (n) of vibration of a string is given as where T is tension and l is the length of vibrating string. Then, the dimensional formula for m is

A
[M⁰L¹T⁰]

B
[M⁰L⁰T⁰]

C
[M¹L⁻¹T⁰]

D
[ML⁰T⁰]

Solution
Question 9
4 / -1

Three particles A, B and C are situated at the vertices of an equilateral triangle of side l at t = 0. The particle A heads towards B, B towards C, C towards A with constant speeds v. Find the time of their meeting.

A
2l/3v

B
3l/2v

C
2l

D
3l/4v

Solution

The motion of the particles is roughly sketched in figure. By symmetry they will meet at the centroid O of the triangle. As the speed of all the particles is equal they will cover equal distance in any given interval of time.

If we join the instantaneous position of the particle at any time, the particles will form an equilateral triangle of same centroid as initial triangle.

The component of the velocity along AO is vcos 30^∘. This component will be equal to the rate of change of distance between A and O.

At t = 0, distance between A and O
Question 10
4 / -1

The P−V equation for a process of an ideal gas is given as

The graphical representation of the above process is shown as

A

B

C

D

Solution