Download App

1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
The potential energy of a particle varies with distance $x$ from a fixed origin as $U=\frac{A \sqrt{x}}{x^2+B}$, where $A$ and $B$ are dimensional constants then dimensional formula for $A B$ is
  • ✓
    $\left[ ML ^{11/2} T ^{-2}\right]$
  • B
    $\left[ ML ^{7 / 2} T ^{-2}\right]$
  • C
    $\left[M^2 L^{9 / 2} T^{-2}\right]$
  • D
    $\left[ ML ^{13 / 2} T ^{-3}\right]$
✓

Answer

Correct option: A.
$\left[ ML ^{11/2} T ^{-2}\right]$
a
(a)

$x =$ distance from a fixed origin

$u =\frac{ A \sqrt{ x }}{ x ^2+ B }$

unit of $B$ is same as $x ^2$. Unit of $x ^2=\left[ L ^2\right]$

$B =\left[ L ^2\right]$

$u =\frac{\left[ x ^{1 / 2}\right] A }{ x ^2+ B }$

$A =\frac{ u \left( x ^2+ B \right)}{\sqrt{ x }}=\frac{ kgm }{ s ^2} \times \frac{ m ^2}{ m ^{1 / 2}}$

$A =\frac{ kgm }{ s ^2}$

$A =\left[ ML ^{7 / 2} T ^{-2}\right]$

Dimensions of $AB =\left[ ML ^{7 / 2} T ^{-2}\right]\left[ L ^2\right]$

Dimensions of $AB =\left[ ML ^{11 / 2} T ^{-2}\right]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 1. units,dimensions and measurement→1. units,dimensions and measurement — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is :
→
Newton's first law of motion describes the following
→
The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is ........ $^o$
→
A ball of mass $m$ moving with a velocity $v$ collides with an identical ball at rest. After collision, the first ball comes to rest. The speed of the other ball is:
→
Two identical stringed instruments have frequency $100 Hz$. If tension in one of them is increased by $4\%$ and they are sounded together then the number of beats in one second is
→
A uniform rod of mass $m$, length $L$, area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be
→
In the figure shown, the two projectiles are fired simultaneously. The minimum distance between them during their flight is  ........ $m$
→
A simple harmonic oscillator of angular frequency $2\,rad\,s^{-1}$ is acted upon by an external force $F = sin\,t\,N .$ If the oscillator is at rest in its equilibrium position at $t = 0,$ its position at later times is proportional to
→
A thin uniform rod of length $L$ and certain mass is kept on a frictionless horizontal table with a massless string of length $L$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point $O$. If a horizontal impulse $P$ is imparted to the rod at a distance $x=L / n$ from the mid-point of the rod (see figure), then the rod and string revolve together around the point $O$, with the rod remaining aligned with the string. In such a case, the value of $n$ is. . . . . . 
→
A sphere $P$ of mass $m$ and moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta $ between the velocities of the spheres after the collision shall be ............... $^o$
→