Class 11th

The linear mass density of a thin rod AB of length L varies from A to B as λ(x) = λ₀ (1 + x/L), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:

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Class 11th Physics Motion in Straight Line

Contributor-Level 10

dm = λdx = λ? (1 + x/L)dx
M = ∫? λ? (1 + x/L)dx = λ? [L + L²/2L] = 3λ? L/2
dI = dmx² = λ? (1 + x/L)dx * x²
I = λ? ∫? (x² + x³/L)dx = λ? [L³/3 + L? /4L]
I = (7λ? L³)/12 = (7/12) * (2M/3L) * L³ = (7/18)ML²

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2 months ago

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m ) by the particle during the time interval t = 0 to t = 5 s will be .

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Contributor-Level 10

Distance moved = Area under curve
= ½ * 8 * 5 = 20

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2 months ago

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as:

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Class 11th Physics Mechanical Properties of Fluids

Contributor-Level 10

Mean relaxation time T = λ/V? = λ / √ (8RT/πm)
∴ T ∝ 1/√T

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2 months ago

A cube of metal is subjected to a hydrostatic pressure 4GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, B = 8 * 10¹⁰ Pa)

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Contributor-Level 10

B (ΔV/V) = ΔP
ΔV/V = ΔP/B = (4 x 10? )/ (8 x 10¹? ) = 1/20
V = l³
dV = 3l² dl
dV/V = 3l²dl/l³ = 3dl/l
ΔV/V = 3 (Δl/l); 1/20 = 3 (Δl/l); ΔV/V = 1/60

% (Δl/l) = 100/60 = 1.67%

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2 months ago

Class 11th Thermodynamics

Match the thermodynamics processes taking place in a system with the correct conditions. In the table: ΔQ is the heat supplied, ΔW is the work done and ΔU is change in internal energy of the system. Match the following:

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Class 11th Physics Oscillations

Contributor-Level 10

ΔQ = heat supplied
ΔW = work done
ΔU = change in internal energy
(i) adiabatic (B) Δθ = 0
(ii) isothermal (D) ΔU = 0
(iii) isochoric (A) ΔW = 0
(iv) isobaric (C) ΔU ≠ 0, ΔW ≠ 0, ΔQ ≠ 0

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2 months ago

When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y(t) = y₀sin² ωt, where ' y ' is measured from the lower end of unstretched spring. Then ω is:

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Contributor-Level 10

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2 months ago

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv² where v is it speed. The maximum height attained by the ball is:

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Contributor-Level 10

Mg + MkV² = MA = -mv (dV/dx)
Vdv = (−) (g + kV²)dx
∫? (Vdv)/ (g + kv²) = ∫? - dx
[ln (g + kV²)/2k]? = -x
ln (g/ (g + ku²) = −2kx
x = (1/2k)ln (1 + ku²/g)

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2 months ago

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms⁻¹ at a point where the pressure is P Pascal. At another point where pressure is P/2 Pascal its speed is V ms⁻¹. If the density of the fluid is ρ kgm⁻³ and the flow is streamline, then V is equal to:

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Contributor-Level 10

Using Bernoulli's equation
P? + (1/2)ρv? ² + ρgh? = P? + (1/2)ρv? ² + ρgh?
For horizontal tube h? = h?
P + (1/2)ρv² = P/2 + (1/2)ρV²
(1/2)ρV² = P/2 + (1/2)ρv²
V = √ (P/ρ + v²)

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2 months ago

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is :

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Class 11th Work, Energy and Power

Contributor-Level 10

Escape velocity = √ (2GM/R) = v? f
Orbital speed = √ (GM/R) = V?
V? /V? = 1/√2

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2 months ago

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

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