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

The following figure shows a small spherical ball of mass m rolling down the loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a radius R.
(a) Find the kinetic energy of the ball when it is at a point A where the radius makes an angle θ with the horizontal.
(b) Find the radial and the tangential accelerations of the centre when the ball is at A.
(c) Find the normal force and the frictional force acting on the if ball if H = 60 cm, R = 10 cm, θ = 0 and m = 70 g.

A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?

Find the ratio of the weights, as measured by a spring balance, of a 1 kg block of iron and a 1 kg block of wood. Density of iron = 7800 kg/m³, density of wood = 800 kg/m³and density of air = 1.293 kg/m³. 

A wooden block of mass 0.5 kg and density 800 kg/m³ is fastened to the free end of a vertical spring of spring constant 50 N/m fixed at the bottom. If the entire system is completely immersed in water, find the elongation (or compression) of the spring in equilibrium . 

A wooden block of mass 0.5 kg and density 800 kg/m³ is fastened to the free end of a vertical spring of spring constant 50 N/m¹ fixed at the bottom. If the entire system is completely immersed in water, find the time-period of vertical oscillations of the block when it is slightly depressed and released.

1 kg of ice at 0°C is mixed with 1 kg of steam at 100°C. What will be the composition of the system when thermal equilibrium is reached? Latent heat of fusion of ice = 3.36 × 10³ J kg⁻¹ and latent heat of vaporization of water = 2.26 × 10⁶ J kg⁻¹.

Calculate the time required to heat 20 kg of water from 10°C to 35°C using an immersion heater rated 1000 W. Assume that 80% of the power input is used to heat the water. Specific heat capacity of water = 42000 J kg⁻¹ K⁻¹.

On a winter day the temperature of the tap water is 20°C whereas the room temperature is 5°C. Water is stored in a tank of capacity 0.5 m³ for household use. If it were possible to use the heat liberated by the water to lift a 10 kg mass vertically, how high can it be lifted as the water comes to the room temperature? Take g = 10 m s⁻².

A 50 kg man is running at a speed of 18 km h⁻¹. If all the kinetic energy of the man can be used to increase the temperature of water from 20°C to 30°C, how much water can be heated with this energy?

The track shown is figure is frictionless. The block B of mass 2m is lying at rest and the block A or mass m is pushed along the track with some speed. The collision between Aand B is perfectly elastic. With what velocity should the block A be started to get the sleeping man awakened?  

Consider the situation of the previous problem. Assume that the temperature of the water at the bottom of the lake remains constant at 4°C as the ice forms on the surface (the heat required to maintain the temperature of the bottom layer may come from the bed of the lake). The depth of the lake is 1.0 m. Show that the thickness of the ice formed attains a steady state maximum value. Find this value. The thermal conductivity of water = 0.50 W m⁻¹°C⁻¹. Take other relevant data from the previous problem.

A calorimeter contains 50 g of water at 50°C. The temperature falls to 45°C in 10 minutes. When the calorimeter contains 100 g of water at 50°C, it takes 18 minutes for the temperature to become 45°C. Find the water equivalent of the calorimeter.

You are driving a motorcycle on a horizontal road. It is moving with a uniform velocity. Is it possible to accelerate the motorcycle without putting higher petrol input rate into the engine?

Is it necessary to express all angles in radian while using the equation ω = ω₀ + at ?

A car driver going at some speed v suddenly finds a wide wall at a distance r. Should he apply brakes or turn the car in a circle of radius r to avoid hitting the wall?

Can the centre of mass of a body be at a point outside the body?

The weight Mg of an extended body is generally shown in a diagram to act through the centre of mass. Does it mean that the earth does not attract other particles?

A circular road of radius r is banked for a speed v = 40 km/hr. A car of mass of m attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible. 

(a) The are cannot make a turn without skidding.
(b) If the car turns at a speed less than 40 km/hr, it will slip down.

(c) If the car turns at the car is equal to \[\frac{\text{mv}^2}{\text{r}}\]

(d) If the car turns at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than \[\frac{\text{mv}^2}{\text{r}}\]

If the horizontal force needed for the turn in the previous problem is to be supplied by the normal force by the road, what should be the proper angle of banking?

A park has a radius of 10 m. If a vehicle goes round it at an average speed of 18 km/hr, what should be the proper angle of banking?