The moment of inertia of a uniform cylinder of length

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A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its initial speed is v₀ = 10 ms^–1. If, after 10 s, its energy is 1/8 mv₀²,the value of k will be

• 10^-4 kg m^-1

• 10^–1 kg m^–1 s^–1

• 10^-3 kg m^-1

• 10^-3 kg m^-1

A slender uniform rod of mass M and length

The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius)

5.

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths λ_A to λ_B after the collision is

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A time-dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be

• 9J

• 18 J

• 4.5 J

• 4.5 J

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

A particle is executing simple harmonic motion with a time period T. AT time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like 

The temperature of an open room of volume 30 m³ increases from 17°C to 27°C due to sunshine. The atmospheric pressure in the room remains 1 × 105 Pa. If ni and n_f are the numbers of molecules in the room before and after heating, then n_f – n_i will be

• 2.5 x 10²⁵

• -2.5 x 10²⁵

• -1.61 x 10²³

• -1.61 x 10²³

The following observations were taken for determining surface tension T of water by the capillary method :
Diameter of capillary, D = 1.25 × 10^–2 m rise of water, h = 1.45 × 10^–2 m
Using g = 9.80 m/s2 and the simplified relation T = (rhg/2) x103 n/m, the possible error in surface tension is closest to:

• 2.4%

• 10%

• 0.15%

• 0.15%