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

A room has a window fitted with a single 1.0 m × 2.0 m glass of thickness 2 mm. (a) Calculate the rate of heat flow through the closed window when the temperature inside the room is 32°C and the outside is 40°C. (b) The glass is now replaced by two glasspanes, each having a thickness of 1 mm and separated by a distance of 1 mm. Calculate the rate of heat flow under the same conditions of temperature. Thermal conductivity of window glass = 1.0 J s⁻¹ m⁻¹°C⁻¹ and that of air = 0.025 m^-1°C^-1 .

Four identical rods AB, CD, CF and DE are joined as shown in following figure . The length, cross-sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperature T₁, T₂ and T₃ respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

Following figure  shows two adiabatic vessels, each containing a mass m of water at different temperatures. The ends of a metal rod of length L, area of cross section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is s. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.

A calorimeter of negligible heat capacity contains 100 cc of water at 40°C. The water cools to 35°C in 5 minutes. The water is now replaced by K-oil of equal volume at 40°C. Find the time taken for the temperature to become 35°C under similar conditions. Specific heat capacities of water and K-oil are 4200 J kg⁻¹ K⁻¹ and 2100 J kg⁻¹ K⁻¹respectively. Density of K-oil = 800 kg m⁻³.

Which of the following pairs of physical quantities does not have same dimensional formula?

If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula ______.

The displacement of a progressive wave is represented by y = A sin(ωt – kx), where x is distance and t is time. Write the dimensional formula of (i) ω and (ii) k.

In Figure, the co-efficient of friction between the floor and the body B is 0.1. The co-efficient of friction between the bodies B and A is 0.2. A force F is applied as shown on B. The mass of A is m /2 and of B is m. Which of the following statements are true?

1. The bodies will move together if F = 0.25 mg.
2. The body A will slip with respect to B if F = 0.5 mg.
3. The bodies will move together if F = 0.5 mg.
4. The bodies will be at rest if F = 0.1 mg.
5. The maximum value of F for which the two bodies will move together is 0.45 mg.

Mass m₁ moves on a slope making an angle θ with the horizontal and is attached to mass m₂ by a string passing over a frictionless pulley as shown in figure. The coefficient of friction between m₁ and the sloping surface is µ.

1. If m₂ > m₁ sin θ, the body will move up the plane.
2. If m₂ > m₁ (sin θ + µ cos θ), the body will move up the plane.
3. If m₂ < m₁ (sin θ + µ cos θ), the body will move up the plane.
4. If m₂ < m₁ (sin θ − µ cos θ), the body will move down the plane.

Why are mountain roads generally made winding upwards rather than going straight up?

Two masses of 5 kg and 3 kg are suspended with help of massless inextensible strings as shown in figure. Calculate T₁ and T₂ when whole system is going upwards with acceleration = 2 ms² (use g = 9.8 ms^–2).

A block of mass M is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is µ and the acceleration due to gravity is g, calculate the minimum force required to be applied by the finger to hold the block against the wall?

A person in an elevator accelerating upwards with an acceleration of 2 ms^–2, tosses a coin vertically upwards with a speed of 20 ms¹. After how much time will the coin fall back into his hand? ( g = 10 ms^–2)

A rectangular box lies on a rough inclined surface. The co-efficient of friction between the surface and the box is µ. Let the mass of the box be m.

1. At what angle of inclination θ of the plane to the horizontal will the box just start to slide down the plane?
2. What is the force acting on the box down the plane, if the angle of inclination of the plane is increased to α > θ ?
3. What is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed?
4. What is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration a?

The potential energy function for a particle executing linear SHM is given by `V(x) = 1/2 kx^2` where k is the force constant of the oscillator (Figure). For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches `x = ±x_m`. If V and K indicate the P.E. and K.E., respectively of the particle at `x = +x_m`, then which of the following is correct?

A body is moved along a closed loop. Is the work done in moving the body necessarily zero? If not, state the condition under which work done over a closed path is always zero.

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 50,000 kg is moving with a speed of 36 km h^–1 when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, calculate the spring constant.

A curved surface is shown in figure. The portion BCD is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from A which is at a slightly greater height than C.

With the surface AB, ball 1 has large enough friction to cause rolling down without slipping; ball 2 has a small friction and ball 3 has a negligible friction.

1. For which balls is total mechanical energy conserved?
2. Which ball (s) can reach D?
3. For balls which do not reach D, which of the balls can reach back A?

Two identical steel cubes (masses 50 g, side 1 cm) collide head-on face to face with a speed of 10 cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y = 2 × 10¹¹ N/m².

The centre of gravity of a body on the earth coincides with its centre of mass for a ‘small’ object whereas for an ‘extended’ object it may not. What is the qualitative meaning of ‘small’ and ‘extended’ in this regard? For which of the following the two coincides? A building, a pond, a lake, a mountain?