The document Unit & Dimensions Vectors(Part- 3) - Physics, Solution by DC Pandey NEET Notes | EduRev is a part of the NEET Course DC Pandey (Questions & Solutions) of Physics: NEET.

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**Section-IISubjective Questions **

**Ques 1: Youngâ€™s modulus of steel is 2.0 x 10 ^{11} N / m^{2}. Express it in dyne/cm^{2}.**

Ans:

Sol: [wt] = [M

[**Î¸**] = [M^{0}L^{0} T^{0}]**Ques 4: The relation between the energy E and the frequency v of a photon is expressed by the equation E = hv, where h is Planckâ€™s constant. Write down the SI units of h and its dimensions.****Ans:****Ques 5: Write the dimensions of a and b in the relation.****where P is power, x is distance and t is time.****Ans: **[b] = [x^{2}] = [L^{2}]**Ques 6: Check the correctness of the relation where u is initial velocity, a is acceleration and S _{t} is the displacement of by the body in t^{th }second.**

Here t in second. Hence the given equation seems to be dimensionally incorrect. But it is correct because 1 is hidden.

Here k = a dimensionless constant

âˆ´ [E] = [m]^{x} [n]^{y} [a]^{z}

âˆ´ [ML^{2} T^{â€“2}] = [M]^{x}[T^{â€“1}]^{y}[L]^{z}

âˆ´ x = 1, y = 2 and z = 2**Ques 11: The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and radius r of the circle. Derive the formula for F using the method of dimensions.**

**Ans: ****(k = a dimensionless constant) **

Solving we get,

x = 1, y = 2 and z = - 1

âˆ´ **Ques 12: Taking force F, length L and time T to be the fundamental quantities, find the dimensions of (a) density, (b) pressure, (c) momentum and (d) energy.****Ans: **[d] = [F]^{x} [L]^{y} [T]^{z}

âˆ´ [ML^{â€“3}] = [MLT^{â€“2}]^{x}[L]^{y}[T]^{z}

Equating the powers we get,

x = 1, y = - 4, z = 2

âˆ´ [ d] = [FL^{â€“4} T^{2}]

Similarly other parts can be solved.

__Vectors__

**Ques 13: Find the cosine of the angle between the vectors ****Ans: ****Ques 14: Obtain the angle between ****Ans: ****Angle between ****Ques 15: Under what conditions will the vectors be perpendicular to each other ?****Ans: **Their dot product should be zero.**Ques 16: Deduce the condition for the vectors ****Ans: **Ratio of coefficients of should be same.**Ques 17: Three vectors which are coplanar with respect to a certain rectangular co-ordinate system are given by****Find****(c) Find the angle between ****Ans: **No solution is required.**Ques 18: Find the components of a vector along the directions of **

**Ans: ****Ques 19: If vectors be respectively equal to Find the unit vector parallel to **

**Ans:**

**Ques 20: ****If two vectors are By calculation, prove that **

** is perpendicular to both ****Ans: ****Ques 21: Find the area of the parallelogram whose sides are represented by **** Ans: **Area of parallelogram

Applying sine law, we have

**Ques 25: Four forces of magnitude P, 2P, 3P and AP act along the four sides of a square ABCDm cyclic order. Use the vector method to find the resultant force.****Ans: ****Ques 26: ****R ^{2} + S^{2} = 2(P^{2} + Q^{2})**

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