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Page 1 of 33, FUNDAMENTAL OF PHYSICS, for IIT-JEE, NEET, 11th & 12th, Q-1: State whether the following physical quantities are scalar or vector., (i) Mass, (ii) Volume, (iii) Speed, (iv) Acceleration, (v) Density, (vi) Number of moles, (vii) Velocity, (viii) Angular frequency, (ix) Displacement, (x) Angular velocity, Solution:, Scalar: Density, mass, speed, volume, angular frequency, number of moles., Vector: Velocity, acceleration, angular velocity, displacement., A scalar quantity depends only on the magnitude and it is independent of the direction. Density, mass,, speed, volume, angular frequency and number of moles are scalar quantities., as well as the direction. Velocity, acceleration, angular, A vector quantity depends on the magnitud, velocity, displacement comes under this, Q-2: From the following pick any two scalar quantities:, Force, angular momentum, work, current, linear momentum, electric field, average velocity,, magnetic moment, relative velocity., Solution:, The dot product of force and displacement is the work done. Work is a scalar quantity since dot product, of two quanti, is always scalar., scalar quantity as it is described only by its magnitude and it is independent of direction., Q-3: From the following identify the vector quantities:, Pressure, temperature, energy, time, gravitational potential, power, total path length, charge,, coefficient of friction, impulse., Solution:, Impulse is the product of force and time. Since force is a vector quantity, its product with time which is a, scalar quantity gives a vector quantity., for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734), UNAENTACOF PHYSICS
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Page 2 of 33, FUNDAMENTAL OF PHYSICS, for IIT-JEE, NEET, 11th & 12th, Q-4: State with reasons, whether the following algebraic operations with scalar and vector, physical quantities are meaningful:, (a) Addition of any two scalars, (b) Adding a scalar to a vector which has the same dimensions, (c) Multiplying a vector by any scalar, (d) Multiplying any two scalars, (e) Adding any two vectors, (f) Addition of a vector component to the same vector., Solution:, (a) Meaningful:, The addition of two scalar quantities is meaningful only if they both represent the same physical, quantity., (b) Not Meaningful:, The addition of a vector quantity with a scalar quantity is not meaningful, (c) Meaningful:, A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse., (d) Meaningful:, A scalar, irrespective of the physical qu:, the same or different dimensions., it represents, can be multiplied by another scalar having, (e) Meaningful:, The addition of two vector, tities is meaningful only if they both represent the same physical, quantity., (f) Meaningful:, A component of a, tor can be added to the same vector as they both have the same dimensions., NBAMENTÀL OF PHYSICS, Q-5: Read each statement below carefully and state with reasons, if it is true or false:, (a) The magnitude of a vector is always a scalar, (b) Each component of a vector is always a scalar, (c) The total path length is always equal to the magnitude of the displacement vector of a, particle, (d) The average speed of a particle (defined as total path length divided by the time taken to, cover the path) is either greater or equal to the magnitude of the average velocity of the particle, over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector., for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734)
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Page 3 of 33, FUNDAMENTAL OF PHYSICS, for IIT-JEE, NEET, 11th & 12th, Solution:, (a) True:, The magnitude of a vector is a number. So, it is a scalar., (b) False:, Each component of a vector is also a vector., (c) False:, The total path length is a scalar quantity, whereas displacement is a vector quantity. Hence, the total, path length is always greater than the magnitude of displacement. It becomes equal to the magnitude, of displacement only when a particle is moving in a straight line., (d) True:, It is because of the fact that the total path length is always greater, displacement of a particle., or equal to the magnitude of, (e) True:, Three vectors, which do not lie in a plane, cannot be represented by the sides of a triangle taken in the, same order., Q-6: Establish the following vector inequalities geometrically or otherwise:, (a) la +히 < lal+ |0, (b) la-비> |lal-1해, (c) la-b| < lal+, T|al-|b||, ÙNDAMENTA OE PHYSIC, When does the equality sign above apply?, Solution:, (a) Let two vectors a and b be represented by the adjacent sides of a parallelogram PQRS, as given in the, figure., for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734)
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Page 4 of 33, FUNDAMENTAL OF PHYSICS, for IIT-JEE, NEET, 11th & 12th, R, Б, Here,, QR = ja| –0, (i), |#s| - |P| - | –, =, - (ii), ä + b - (ii), Each side in a triangle is smal, rthan the sum of the other two sides., Therefore, in AQI, QS < (QR, NDAMENTAL OF PHYSICS, la + |히-(iv), If the two vectors a and b act along a straight line in the same direction, then:, |a + 5| = 1a|+ |5|, (V), Combine equation (iv) and (v),, for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734)
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Page 5 of 33, FUNDAMENTAL OF PHYSICS, for IIT-JEE, NEET, 11th & 12th, Ja +5| < ja| + |5|, (b) Let two vectors a and b be represented by the adjacent sides of a parallelogram PQRS, as given in the, figure., S, a + 5, P., a, Here,, QR, |īs| = |ie|, -(ii), - (II), Each side in a triangle is smaller than the sum of the other two sides., Therefore, in AQRS,, QS + RS > QR, QS + QR > RS, for IIT-JEE, NEET, 11th & 12th, R.K.Sharma (8507152734), FỪNDAMENTAL OE PHYSICS
