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

The shells of crabs found around a particular coastal location in Japan seem mostly to resemble the legendary face of a Samurai. Given below are two explanations of this observed fact. Which of these strikes you as a scientific explanation ? 

(a) A tragic sea accident several centuries ago drowned a young Samurai. As a tribute to his bravery, nature through its inscrutable ways immortalized his face by imprinting it on the crab shells in that area.

(b) After the sea tragedy, fishermen in that area, in a gesture of honor to their dead hero, let free any crab shell caught by them which accidentally had a shape resembling the face of a Samurai. Consequently, the particular shape of the crab shell survived longer and therefore in course of time the shape was genetically propagated. This is an example of evolution by artificial selection. 

[Note : This interesting illustration taken from Carl Sagan’s ‘The Cosmos’ highlights the fact that often strange and inexplicable facts which on the first sight appear ‘supernatural’ actually turn out to have simple scientific explanations. Try to think out other examples of this kind].

A physical quantity P is related to four observables a, b, c and d as follows:

`P = (a^3b^2)/((sqrtcd))`

The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result?

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):

the total mass of rain-bearing clouds over India during the Monsoon

`hati  "and"  hatj` are unit vectors along x- and y-axis respectively. What is the magnitude and direction of the vectors `hati+hatj` and `hati-hatj` ? What are the components of a vector `A = 2hati + 3hatj` along the directions of `hati + hatj` and `hati - hatj` ? [You may use graphical method]

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?

State if the following statement is true or false. Give a reason for your answer.

Work done in the motion of a body over a closed loop is zero for every force in nature.

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by

`F = -hati+2hatj+3hatkN`

Where `hati,hatj,hatk` are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis ?

A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 ms^–1. How long does the body take to stop?

A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m s^–2. Calculate the initial thrust (force) of the blast.

A body of mass 0.40 kg moving initially with a constant speed of 10 m s^–1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.

A man of mass 70 kg stands on a weighing scale in a lift which is moving

1. upwards with a uniform speed of 10 m s-¹
2. downwards with a uniform acceleration of 5 m s^–2
3. upwards with a uniform acceleration of 5 m s^–2. What would be the readings on the scale in each case?
4. What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

The below figure shows the position-time graph of a particle of mass 4 kg.

1. What is the force on the particle for t < 0, t > 4 s, 0 < t < 4 s?
2. What is the impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only.)

Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to

1. A,
2. B along the direction of string. What is the tension in the string in each case?

Two masses 8 kg and 12 kg are connected at the two ends of a light, inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)

Explain why a cricketer moves his hands backwards while holding a catch.

A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative]

 T₁ and v₁ denote the tension and speed at the lowest point. T₂ and v₂ denote corresponding values at the highest point.

A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m s^–2. The crew and the passengers weigh 300 kg. Give the magnitude and direction of the

(a) force on the floor by the crew and passengers,

(b) action of the rotor of the helicopter on the surrounding air,

(c) force on the helicopter due to the surrounding air.

An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop?

A monkey of mass 40 kg climbs on a rope in given Figure which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey

(a) climbs up with an acceleration of 6 m s^–2

(b) climbs down with an acceleration of 4 m s^–2

(c) climbs up with a uniform speed of 5 m s^–1

(d) falls down the rope nearly freely under gravity?

(Ignore the mass of the rope).