NCERT Solutions for Class 11-science Physics Chapter 4 - Motion in a Plane

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Chapter 4 - Motion in a Plane Exercise 85

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(a)The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.


(b)The addition of a vector quantity with a scalar quantity is not meaningful.

(c) Yes, multiplying a vector by scalar is perfectly meaningful and gives a vector
in output having magnitude scalar times the magnitude of original vector. For example, force is multiplied with time to give impulse.


(d) Yes , product of two scalars is meaningful. For example, V=IR, multiplies scalars current and resistance to give voltage.


(e)The addition is meaningful if both the vectors have same dimensions.

(f)Yes, as both the vectors have same dimensions they can be added to give a vector output.

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Chapter 4 - Motion in a Plane Exercise 86

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Chapter 4 - Motion in a Plane Exercise 87

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Chapter 4 - Motion in a Plane Exercise 88

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begin mathsize 14px style Given colon
Range comma space straight R equals 3 space km
Angle space of space projection comma space straight theta equals 30 degree
Acceleration space due space to space gravity comma space straight g equals 9.8 space straight m divided by straight s squared
Horizontal space range space for space the space projection space velocity space straight u subscript 0 comma space is space given space by space the space relation colon
straight R equals fraction numerator straight u subscript 0 superscript 2 sin 2 straight theta over denominator straight g end fraction
3 equals fraction numerator straight u subscript 0 superscript 2 over denominator straight g end fraction sin 60 degree
square root of 3 cross times square root of 3 equals fraction numerator straight u subscript 0 superscript 2 over denominator straight g end fraction cross times fraction numerator square root of 3 over denominator 2 end fraction space space space space left square bracket because 3 equals square root of 3 cross times square root of 3 right square bracket
fraction numerator straight u subscript 0 superscript 2 over denominator straight g end fraction equals 2 square root of 3 space space space space space space... space left parenthesis 1 right parenthesis
The space maximum space range space left parenthesis straight R subscript max right parenthesis space is space achieved space by space bullet space when space it space is space fired space at space an space angle space of space 45 degree space with space the space horizontal comma space that space is comma
straight R subscript max equals fraction numerator straight u subscript 0 superscript 2 over denominator straight g end fraction space space space space space space space... space left parenthesis 2 right parenthesis
On space comparing space equations space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get comma
straight R subscript max equals 2 square root of 3 equals 2 cross times 1.732 equals 3.46 space km
Hence comma space there space is space no space way space one space can space hope space to space hit space the space target space 5 space km space away. end style

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