Question 2 :
In a system of units if force F, acceleration A and time T are taken as fundamental units, then the dimensional formula of energy is
Question 4 :
In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10g and 0.1s respectively. The unit of force in this system will be equivalent to -
Question 5 :
A balance has pans of unequal weight but arms are of equal length. The weight of body in one pan is measured as 8 kg and when pans are interchanged the weight of body measured is 18 kg. The true weight of body is -
Question 7 :
An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is
Question 9 :
The dimensions of {tex} \frac { a } { b } {/tex} in the equation {tex} P = \frac { a - t ^ { 2 } } { b x } , {/tex} where {tex} P {/tex} is pressure, {tex} x {/tex} is distance and {tex} t {/tex} is time, are
Question 12 : If h is height and g is acceleration due to gravity, then the dimensional formula of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c51d491ec9580069739b' height='44' width='32' > is the same as that of -
Question 14 :
A wave is represented by y = a sin (At - Bx + C) where A, B, C are constants. The Dimensions of A, B, C are (here y and x are displacement and distance and t is time) -
Question 17 :
If {tex} | \vec { A } \times \vec { B } | = \sqrt { 3 } \vec { A } \cdot \vec { B } , {/tex} then the value of {tex} | \vec { A } + \vec { B } | {/tex} is
Question 20 :
A force {tex} F {/tex} is given by {tex} F = a t + b t ^ { 2 } {/tex} where {tex} t {/tex} is time, what are the dimension of {tex} a {/tex} and {tex} b ? {/tex}
Question 21 :
The force {tex} F {/tex} on a sphere of radius '{tex}a{/tex}' moving in a medium with velocity {tex} ^ { \prime } v ^ { \prime } {/tex} is given by {tex} F = 6 \pi \eta a v {/tex}. The dimensions of {tex} \eta {/tex} are
Question 22 :
{tex}\mathbf {Assertion}{/tex} : The quantity {tex} (1/ \sqrt{ \mu _0 \epsilon_0}){/tex} is dimensionally equal to velocity and numerically equal to velocity of light.<br>{tex}\mathbf {Reason}{/tex} : {tex} \mu_0{/tex} is permeability of free space and {tex}\epsilon_0{/tex} is the permittivity of free space.
Question 23 :
If {tex}P, Q, R{/tex} are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
Question 26 :
The dimensional formula of [ML<sup>-1</sup>T <sup>-2</sup>] does not represent the following -
Question 27 :
The correct value of {tex} 0 ^ { \circ } \mathrm { C } {/tex} on the Kelvin scale is
Question 28 : The area of the parallelogram represented by the vectors <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c5974389b1556ddef554' height='24' width='63' > and <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c597491ec95800697427' height='24' width='55' > is-
Question 30 : For a body moving along x-axis, the distance travelled by body from a reference point is given as function of time t as x = at<sup>2</sup> + b, where a and b are constants, then the dimension of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c603491ec9580069748f' height='23' width='28' > is same as -
Question 31 :
A dust particle oscillates in air with a time period which depends on atmospheric pressure P, density of air d and energy of the particle E, then time period is proportional to
Question 32 :
Find a vector {tex} \vec { x } {/tex} which is perpendicular to both {tex} \vec { A } {/tex} and {tex} \vec { B } {/tex} but has magnitude equal to that of {tex} \vec { B } {/tex} . Rule: Inter change coeff. of {tex} \hat { i } {/tex} and {tex} \hat { j } {/tex} and change sign of one of the vectors. {tex} \vec { A } = 3 \hat { i } - 2 \hat { j } + \hat { k } , \vec { B } = 4 \hat { i } + 3 \hat { j } - 2 \hat { k } {/tex}
Question 33 :
Which of the following units denotes the dimensions {tex} \left[ M L ^ { 2 } / Q ^ { 2 } \right] , {/tex} where {tex} Q {/tex} denotes the electric charge?
Question 34 :
If velocity {tex} v {/tex}, acceleration {tex} A {/tex} and force {tex} F {/tex} are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of {tex} v , A {/tex} and {tex} F {/tex} would be
Question 35 :
{tex} E , m , l {/tex} and {tex} G {/tex} denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of {tex} \frac { E l ^ { 2 } } { m ^ { 5 } G ^ { 2 } } {/tex} are
Question 36 :
If the dimensions of length are expressed as {tex} G ^ { x } c ^ { y } h ^ { z } {/tex}; where {tex} G , c {/tex} and {tex} h {/tex} are the universal gravitational constant, speed of light and Planck's constant respectively, then
Question 37 : In Fig. shown find the velocity of block {tex} m {/tex} if both the rope ends are pulled with {tex} a {/tex} velocity {tex} v {/tex} .<br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e8ac286131a2b237d875c76' class="uploaded-image" />
Question 38 :
The acceleration of a particle as seen from two frames {tex} S _ { 1 } {/tex} and {tex} S _ { 2 } {/tex} has equal magnitude {tex} 5 \mathrm { ms } ^ { - 2 } . {/tex}
Question 40 :
If the constant of gravitation {tex} ( G ) , {/tex} Planck's constant {tex} ( h ) {/tex} and the velocity of light {tex} ( c ) {/tex} be chosen as fundamental units. The dimension of the radius of gyration is
Question 45 :
The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of
Question 47 :
{tex}\mathbf {Assertion}{/tex} : : Mass, length and time are fundamental physical quantities. <br>{tex}\mathbf {Reason}{/tex} : They are independent of each other.
Question 48 :
The equation of a wave is y = a sin (At - Bx + C), where A, B and C are constants. The dimensions of A, B and C are respectively
Question 49 :
The dimensions of h/e (h = Planck's constant and e = electronic charge) are same as that of :
Question 51 : Match the Column I with Column II <table><tr><th>Column I Physical quantity</th> <th>Column II Name of unit</th> </tr><tr><td>(A) Conductance</td> <td>(p) Gray</td> </tr> <tr><td>(B) Magnetic induction </td> <td>(q) Lumen</td> </tr> <tr><td>(C) Absorbed dose</td> <td>(r) Tesla</td> </tr> <tr><td>(D) Luminous flux</td> <td>(s) Siemens</td></tr></table>
Question 52 :
Calculate the area of the triangle determined by the two vectors {tex} \vec { A } = 3 \hat { i } + 4 \hat { j } {/tex} and {tex} \vec { B } = - 3 \hat { i } + 7 \hat { j } {/tex}
Question 53 :
The value of {tex} n {/tex} so that vectors {tex} 2 \hat { i } + 3 \hat { j } - 2 \hat { k } , 5 \hat { i } + n \hat { j } + \hat { k } {/tex} and {tex} - \hat { i } + 2 \hat { j } + 3 \hat { k } {/tex} may be coplanar, will be
Question 54 : The velocity of a particle is given by v = a + <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75c571b5f89758f2d4e454' height='37' width='15' > + ct<sup>2</sup><br>The unit of b will be
Question 55 :
Dimensions of one or more pairs are same. Identify the pairs-
