Questions on Vector analysis

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Instructor: Saurabh verma

B.Tech, IIT Kanpur

mob: 09956551609

Q.1: What do you understand by scalar quantities and vector quantities? Explain with example.

Q.2: If two vectors A and B are acting at a point with angle q. Derive an equation for magnitude and direction of resultant R using Parallelogram method.

Q.3: Resultant of two vectors P and Q is R if we reverse the direction of Q then resultant becomes S. Prove

R² + S² = 2 (P² + Q²)

Q.4: If ABCDEF is a regular hexagon, prove the followings:

AB + AC + AD + AE + AF = 3 AD

Q.5: If | A X B | = Ö3 A – B, find out the value of A + B.

Q.6: If A = 3 i + 5 j, B = 2 i + 4 j ; Find out the followings:

1. Angle between A and B
2. A.B
3. A X B
4. (A + B). B

Q.7: If P X Q = R, state the true/false about the followings:

1. R is perpendicular to P
2. R is perpendicular to Q
3. R is perpendicular to (P + Q)
4. R is perpendicular to (P X Q)

Q.8: If two force of magnitude 6 N and 8 N acting on a point with angle 60^o. Find out the magnitude and direction of resultant.

Q.9: If magnitude of two perpendicular vectors P and Q is 5 and 7 respectively. Use vector diagram to show the P + Q and P – Q and find out the magnitude and direction.

Q.10: A car is moving on horizontal ground with velocity V m/s. The driver of car observes the rain to be falling vertically downwards with velocity 2V m/s. What is the velocity and direction of the rain?

Q.11: A man is swimming across a river at angle of 120^o. He took 100 seconds in crossing the river which is 10 m wide. Find out the followings:

1. Flow velocity of river
2. Speed of swimmer

Questions on Projectile motion

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Instructor: Saurabh verma

B.tech, IIT Kanpur

mob: 09956551609

Q.1: What is projectile motion? Prove that its trajectory is a parabola.

Q.2: In a projectile motion, a particle is thrown with velocity u making an angle q with horizontal. Derive the formula for maximum height, flight time and range.

Q.3: A canon is placed on a tower of height 100 m. The canon is fired at angle 30^o with horizontal and velocity 1000 m/s. Find out-

1. Time required to attain maximum height
2.  Total flight time
3. Final velocity at which the ball will strike the ground
4. Maximum height of the projectile
5. The range of the projectile

Q.4: A man sees a bird at the height of 39.6 m and 59.2 m far from the man on the tree. He fires at an angle of 45^o. Find out:

1. What would be the velocity of bullet
2. After how much time bullet will hit the bird

Q.5: If two balls are projected with same velocity and different angle and they achieve the same range. Flight time of balls is T₁ and T₂ respectively. Prove

T₁.T₂= 2R/g

Q.6: A stone is thrown at velocity 10 m/s with 60^o horizontal angle. If the range of projectile is 10Ö3 m, find out the height of tower.

Q.7: If the maximum velocity of a canon is V, what will be the maximum area that can be protected by this canon?

Q.8: A monkey is seated upon tree of height H and point of shooting is x meter far from the base of tree. Will the man can kill the monkey if his target is at monkey and

1. Monkey remain seated at tree
2. Monkey is falling freely 

Question on "Motion in straight line"

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Instructor: Saurabh verma

B.Tech, IIT Kanpur

Mob: 09956551609

Q.1: For an object projected upward with a velocity V_o, which comes back to the same point after some time, Draw

1. Acceleration time graph
2. Position time graph
3. Velocity time graph

Q.2: Derive the equations of motion for an object moving with constant acceleration along a straight line.

Q.3: Justify your answer with example. Will there be any acceleration in the particle if

1. Velocity of particle is zero.
2. Speed of particle is constant.
3. Velocity of particle is constant.

Q.4: What is the difference between the followings?

1. Distance and displacement
2. Speed and velocity

Q.5: if displacement of the particle is given by equation s = t³ - 6t² + 3t + 4 find out the speed at which acceleration is zero.

Q.6: A particle moves at 5 km/hr for 10 minutes, at 10 m/s for 60 seconds, at 4 km/s for 120 second. Find the average velocity and draw velocity vs time curve.

Q.7: A balloon is moving upward with speed of 10 m/s. at the height of 400 m, a stone is released from it. How much time will the stone take to strike the ground?

Q.8: From the height of 200 m, a stone is released and another stone is thrown upwards with velocity 50 m/s simultaneously. After how much time they cross each other and at which height?

Q.9: A police jeep is chasing with velocity of 45 km/hr a thief in another jeep moving with velocity 53 km/hr. Police fires a bullet with velocity 180 m/s. find out the velocity at which it will strike the thief.

Q.10: A particle with initial velocity 200 cm/s and retardation 10 cm/s² completes the displacement of 1500 cm. How much time it will take to complete? Give reasons for two answers.

Questions on Dimension Analysis

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Instructor: Saurabh Verma

Mob: +91 9956551609

Q.1: Define the term 'Dimension'. Give the example of three dimensionless quantities.

Q.2: Define the 'principle of homogeneity of dimensions'.

Q.3: List all the fundamental quantities and their units.

Q.4: What are uses of dimensional analysis? What are limitation of dimension analysis?

Q.5: A book with many printing errors contains four different formulas for the displacement 'y' of a particle undergoing a certain periodic motion:

1. y = a sin (2πt/T)
2. y = a sin (vt)
3.  y = (a/T) sin (t/a)
4.  y = (a/2) (sin (2πt/T) + cos(2πt/T) )

Where a: maximum displacement of the particle, v: speed of the particle and T= time period of motion. Rule out the wrong formulas on dimensional ground.

Q.6: If dimension of A and B are different, which of the followings is possible?

1. A+B
2. A-B
3. A/B
4. A/e^AB

Q.7: Compute the dimension of the followings:

1. Voltage
2. Resistance
3. Pressure
4. Gas constant

Q.8: Convert followings using method of dimensions.

1. 10 dyne into Newton.
2. One erg into joules.

Q.9: A student while doing an experiment finds that the velocity of an object varies with time and it can be expressed as equation:

v = Xt² + Y/(A+g) + Z

if units of v, t and g expressed in SI units, determine the unit of constants X, Y, A and Z.

Q.10: If Force (F), Velocity (V) and Acceleration (A) are taken as the fundamental units instead of mass, length and time, express Pressure and impulse in terms of given fundamental units.

Q.11: Which of the following pairs has the same dimensions?

1. Specific heat and latent heat
2. Impulse and momentum
3. Surface tension and force
4. Moment of inertia and torque

Q.12: In Formula tan (mx/ac) = be^ct, m is mass, x is displacement and t is time. Find out the dimension of a, b and c.

Q.13: The speed of sound v in a gas depends on the pressure p, the density r and the volume V of the gas. Find out the appropriate formula for speed of sound.

"Practice makes a man perfect"

Questions on Error analysis

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Instructor: Saurabh Verma

Mob: +91 9956551609

Q.1: Define accuracy and precision. Can we say an instrument of high precision is accurate? Justify your answer.

Q.2: Define "absolute error", "relative error" and "least count".

Q.3: If percentage error in radius of a sphere is 5%, find out percentage error in surface area and volume?

Q.4: Which is most precise in the given readings 4567g, 456.7g, 45.67g, 4.567g?

Q.5: Measured lengths by an instrument are 25.0cm and 10.0cm. Which one is more accurate and why?

Q.6: A rectangular board is measured with a scale having accuracy of 0.2cm. The length and breadth are measured as 35.4 cm and 184 cm respectively. Find the relative error and percentage error of the area calculated.

Q.7: Percentage error in volume of a cube is 9%. Find the percentage error in side of the cube.

Q.8: In an experiment, value of resistances are R₁= 5.0 ± 0.2 Ω and R₂= 10.0 ± 0.1 Ω. Find out the percentage error in (R₁+R₂) and in (R₁.R₂/ (R₁+R₂)).

"Practice makes a man perfect"