Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

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?

The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point?

For an ideal liquid ______.

1. the bulk modulus is infinite.
2. the bulk modulus is zero. 
3. the shear modulus is infinite.
4. the shear modulus is zero.

For an ideal liquid ______.

1. the bulk modulus is infinite.
2. the bulk modulus is zero. 
3. the shear modulus is infinite.
4. the shear modulus is zero.

What is the Bulk modulus for a perfect rigid body?

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is 9.8 × 10⁸ Nm^–2; and the density of sea water is 10³ kg m^–3.)

With increase in temperature, the viscosity of ______.

1. gases decreases.
2. liquids increases.
3. gases increases.
4. liquids decreases.

Is viscosity a vector?

Heat is associated with ______.

These days people use steel utensils with copper bottom. This is supposed to be good for uniform heating of food. Explain this effect using the fact that copper is the better conductor.

We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their lengths remain constant. If α_iron = 1.2 × 10⁻⁵/K and α_brass = 1.8 × 10⁻⁵/K, what should we take as length of each strip?

A thin rod having length L₀ at 0°C and coefficient of linear expansion α has its two ends maintained at temperatures θ₁ and θ₂, respectively. Find its new length.

According to Stefan’s law of radiation, a black body radiates energy σT⁴ from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10^–8 W/m²K⁴ is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When detonated, it reaches temperature of 106 K and can be treated as a black body.

1. Estimate the power it radiates.
2. If surrounding has water at 30°C, how much water can 10% of the energy produced evaporate in 1s?  [S_w = 4186.0 J/kg K and L_v = 22.6 × 10⁵ J/kg]
3. If all this energy U is in the form of radiation, corresponding momentum is p = U/c. How much momentum per unit time does it impart on unit area at a distance of 1 km?

What is the ratio between the distance travelled by the oscillator in one time period and amplitude?