Science (English Medium) Class 11 - CBSE Question Bank Solutions

A steel wire of mass µ per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains << longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m^–3 (Young’s modules Y = 2 × 1011 Nm^–2).

If the yield strength of steel is 2.5 × 10⁸ Nm^–2, what is the maximum weight that can be hung at the lower end of the wire?

A steel rod of length 2l, cross sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young’s modulus for steel, find the extension in the length of the rod. (Assume the rod is uniform.)

In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by `(Ypir^4)/(4R) . Y` is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.

In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by `(Ypir^4)/(4R) . Y` is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.

Which of the following diagrams (Figure) does not represent a streamline flow?

Along a streamline ______.

Streamline flow is more likely for liquids with ______.

1. high density.
2. high viscosity.
3. low density.
4. low viscosity.

Refer to the plot of temperature versus time (figure) showing the changes in the state of ice on heating (not to scale).

1. The region AB represents ice and water in thermal equilibrium.
2. At B water starts boiling.
3. At C all the water gets converted into steam.
4. C to D represents water and steam in equilibrium at boiling point.

A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (Figure). If the temperature is increased ______.

Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P₁ and P₂?

An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1 T, and the volume is increased to 1.05 V, the final pressure will be ______.

The molecules of a given mass of a gas have root mean square speeds of 100 ms⁻¹ at 27°C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127°C and 2.0 atmospheric pressure?

Two molecules of a gas have speeds of 9 × 10 6 ms⁻¹ and 1 × 106 ms⁻¹, respectively. What is the root mean square speed of these molecules?

A gas mixture consists of molecules of types A, B and C with masses m_A > m_B > m_C. Rank the three types of molecules in decreasing order of average K.E.

A gas mixture consists of molecules of types A, B and C with masses m_A > m_B > m_C. Rank the three types of molecules in decreasing order of rms speeds.

An insulated container containing monoatomic gas of molar mass m is moving with a velocity v_o. If the container is suddenly stopped, find the change in temperature.

Explain why there is no atmosphere on moon.

Consider a rectangular block of wood moving with a velocity v₀ in a gas at temperature T and mass density ρ. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to v₀ is A. Show that the drag force on the block is `4ρAv_0 sqrt((KT)/m)`, where m is the mass of the gas molecule.

Motion of an oscillating liquid column in a U-tube is ______.