Class 11th

ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I?. If part ADE is removed, the moment of inertia of the remaining part about the same axis is NI?/16 where N is an integer. Value of N is

A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K ) of the gas in the vessel will be close to

Blocks of masses m, 2m and 8m are arranged in a line on a frictionless floor. Another block of mass m, moving with speed v along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8 m starts moving the total energy loss is p% of the original energy. Value of ' p ' is close to:

Starting from the origin at time t = 0, with initial velocity 5ĵ ms⁻¹, a particle moves in the x-y plane with a constant acceleration of (10î + 4ĵ)ms⁻². At time t, its coordinates are (20 m, y₀m). The values of t and y₀ are, respectively:

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s?². The density of water is 1gmcm?³ and water offers negligible drag force on the bubble. The mass of the bubble is: (g = 980 cm/s²).

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m ) of the waves are:

Match the Cp/Cv ratio for ideal gases with different type of molecules:
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Match the correct option?

The specific heat of water = 4200 J kg⁻¹ K⁻¹ and the latent heat of ice = 3.4 * 10⁵ J kg⁻¹. 100 grams of ice at 0°C is placed in 200 g of water at 25°C. The amount of ice that will melt as the temperature of water reaches 0°C is close to (in grams):

Dimensional formula for thermal conductivity is (here K denotes the temperature):

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height h/2. The velocity versus height of the ball during its motion may be represented graphically by: