List of top Questions asked in CBSE Class XI

A molecule in a gas container hits a horizontal wall with speed 200 \(m\,s^{-1}\) and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision ? Is the collision elastic or inelastic ?
An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 \(\text {keV}\), and the second with 100 \(\text {keV}\). Which is faster, the electron or the proton ? Obtain the ratio of their speeds. (electron mass = \(9.11\times 10^{-31}\) kg, proton mass = \(1.67\times 10^{-27}\) kg, 1 \(\text {eV}\) = \(1.60\times 10^{-19}\) J)
A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by \(\text F\) = \(-\hat{i}+2\hat j+3\hat k\) where \(\hat i,\hat j,\hat k\) 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 body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the 
  1. work done by the applied force in 10 s, 
  2. work done by friction in 10 s, 
  3. work done by the net force on the body in 10 s, 
  4. change in kinetic energy of the body in 10 s, and interpret your results.
A truck starts from rest and accelerates uniformly at 2.0 \(ms^{-2}\). At t = 10 s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the 
  1. velocity, and 
  2. acceleration of the stone at t = 11s ? 
    (Neglect air resistance.)

Explain why 

(a) The blood pressure in humans is greater at the feet than at the brain 

(b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km 

(c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. If, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks -
For any arbitrary motion in space, which of the following relations are true : 
  1. \(v_{average}\)= \(\bigg(\frac{1}{2}\bigg)\) (\(v\) (\(t_1\) ) + \(v\) (\(t_2\) )) 
  2. \(v_{average}\) = \(\frac{[r(t_2)-r(t_1)]}{(t_2-t_1)}\)
  3. \(v(t)\) = \(v(0)\) + \(at\) 
  4. \(r(t)\) = \(r(0)\) + \(v(0)t+\bigg(\frac{1}{2}\bigg)at^2\)
  5. \(a_{average}\) =\(\frac{[v(t_2)-v(t_2)}{(t_2-t_1)}\) 
    (The ‘average’ stands for average of the quantity over the time interval \(t_1\) to \(t_2\) )
A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 \(m\,s^{-1}\), what is the recoil speed of the gun ?
A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?
Two billiard balls each of mass 0.05 \(\text {kg}\) moving in opposite directions with speed 6 \(\text m \,\text s^{-1}\)collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
A man of mass 70 \(\text {kg}\) stands on a weighing scale in a lift which is moving 
  1. upwards with a uniform speed of 10 \(\text m \,\text s^{-1}\) , 
  2. downwards with a uniform acceleration of 5 \(\text m \,\text s^{-2}\) , 
  3. upwards with a uniform acceleration of 5 \(\text m \,\text s^{-2}\) . 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 ?
A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.
Find the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17.

Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.

Find the mean deviation about the median for the data.13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.
A bob of mass 0.1 \(\text {kg}\) hung from the ceiling of a room by a string 2 \(\text m\) long is set into oscillation. The speed of the bob at its mean position is 1 \(\text m\,\text s^{-1}\). What is the trajectory of the bob if the string is cut when the bob is 
  1. at one of its extreme positions, 
  2. at its mean position.
A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10–2 kg and its linear mass density is 4.0 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?

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

Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all: 

(a) y = 2 cos (3x) sin (10t) 

(b) \(y=2\sqrt{x-vt}\)

(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t) 

(d) y = cos x sin t + cos 2x sin 2t

(i) For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude? Explain your answers. (ii) What is the amplitude of a point 0.375 m away from one end?
The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

The transverse displacement of a string (clamped at its both ends) is given by 

y(x, t) = 0.06 sin \((\frac{2π}{3 }x)\) cos (120 πt) 

where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 ×10–2 kg. 

Answer the following : 

(a) Does the function represent a travelling wave or a stationary wave? 

(b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?

(c) Determine the tension in the string

For the travelling harmonic wave 

y(x, t) = 2.0 cos 2π (10t – 0.0080 x + 0.35) 

where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of 

(a) 4 m, 

(b) 0.5 m, 

(c) \(\frac{λ}{2}\), 

(d) \(\frac{3λ}{4}\)