Suppose the kinetic energy of a body oscillating with amplitude A and at a distance x is given by K - B x - x 2- A 2- The dimensions of B are the same as that ofA- work - timeB- work - distanceC- work - distanceD- work - time

The correct option is B work × distanceGiven the equation nbsp;K=Bxx^2+A^2 From principle of homogeneity ⇒ [K]=[Bxx^2+A^2]=[Bxx^2]=[Bx] ⇒ [B]=[K· x]=K.E × ...

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Standard XII

Physics

Units and Dimensions

Suppose the k...

Question

Suppose the kinetic energy of a body oscillating with amplitude $A$ and at a distance $x$ is given by $K = \frac{B x}{x^{2} + A^{2}}$ . The dimensions of $B$ are the same as that of

work / time

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work \times distance

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work / distance

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work \times time

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Solution

The correct option is B $work \times distance$
Given the equation $K = \frac{B x}{x^{2} + A^{2}}$
From principle of homogeneity-
$\Rightarrow [K] = [\frac{B x}{x^{2} + A^{2}}] = [\frac{B x}{x^{2}}] = [\frac{B}{x}]$
$\Rightarrow [B] = [K \cdot x] = K.E \times distance = work \times distance$

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Similar questions

Q. Suppose the kinetic energy of a body oscillating with amplitude

A

and at a distance

x

is given by

K = \frac{B x}{x^{2} + A^{2}}

. The dimensions of

B

are the same as that of :

Q. Match the Column I with Column II.

	Column I		Column II
(A)	When a body does work against friction, its kinetic energy	(p)	independent of time
(B)	Work done by a body is	(q)	time
(C)	Power of a body varies inversely as	(r)	force must be conservative
(D)	When work done over a closed path is zero	(s)	decreases

Fill in the following blanks with suitable words :

(a) Work is measured as a product of ....................... and ..................

(b) The work done on a body moving in a circular path is .....................

(c) 1 joule is the work done when a force of one ............. moves an object through a distance of one.................. in the direction of .....................

(d) The ability of a body to do work is called .................... The ability of a body to do work because of its motion is called .................

(e) The sum of the potential and kinetic energies of a body is called ......... energy.

Q. Planck's constant has the same dimensions as
(a) force × time
(b) force × distance
(c) force × speed
(d) force × distance time

The work-energy theorem states that the work done by a force on a body is equal to the change in kinetic energy of the body.

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Suppose the kinetic energy of a body oscillating with amplitude A and at a distance x is given by K=Bxx2+A2. The dimensions of B are the same as that of

The correct option is B work × distanceGiven the equation K=Bxx2+A2 From principle of homogeneity- ⇒ [K]=[Bxx2+A2]=[Bxx2]=[Bx] ⇒ [B]=[K⋅x]=K.E × distance=work × distance

Suppose the kinetic energy of a body oscillating with amplitude $A$ and at a distance $x$ is given by $K = \frac{B x}{x^{2} + A^{2}}$ . The dimensions of $B$ are the same as that of

The correct option is B $work \times distance$
Given the equation $K = \frac{B x}{x^{2} + A^{2}}$
From principle of homogeneity-
$\Rightarrow [K] = [\frac{B x}{x^{2} + A^{2}}] = [\frac{B x}{x^{2}}] = [\frac{B}{x}]$
$\Rightarrow [B] = [K \cdot x] = K.E \times distance = work \times distance$