Correct4
Incorrect-1
Energy due to position of a particle is given by, {tex} U = \frac { \alpha \sqrt { y } } { y + \beta } , {/tex} where {tex} \alpha {/tex} and {tex} \beta {/tex} are constants, {tex} y {/tex} is distance. The dimensions of {tex} ( \alpha \times \beta ) {/tex} are
{tex} \left[ M ^ { 0 } L T ^ { 0 } \right] {/tex}
{tex} \left[ M ^ { 1 / 2 } L ^ { 3 / 2 } T ^ { - 2 } \right] {/tex}
{tex} \left[ M ^ { 0 } L ^ { - 7 / 2 } T ^ { 0 } \right] {/tex}
{tex} \left[ M L ^ { 7 / 2 } T ^ { - 2 } \right] {/tex}
Correct4
Incorrect-1
Identify the pair whose dimensions are equal
torque and work
stress and energy
force and stress
force and work
Correct4
Incorrect-1
Dimension of {tex} \frac { 1 } { \mu _ { 0 } \varepsilon _ { 0 } } , {/tex} where symbols have their usual
meaning, are
{tex} \left[ \mathrm { L } ^ { - 1 } \mathrm { T } \right] {/tex}
{tex} \left[ \mathrm { L } ^ { - 2 } \mathrm { T } ^ { 2 } \right] {/tex}
{tex} \left[ \mathrm { L } ^ { 2 } \mathrm { T } ^ { - 2 } \right] {/tex}
{tex} \left[ \mathrm { LT } ^ { - 1 } \right] {/tex}
Correct4
Incorrect-1
The physical quantities not having same dimensions are
torque and work
momentum and planck's constant
stress and young's modulus
speed and {tex} \left( \mu _ { \mathrm { o } } \varepsilon _ { \mathrm { o } } \right) ^ { - 1 / 2 } {/tex}
Correct4
Incorrect-1
Which one of the following represents the correct
dimensions of the coefficient of viscosity?
{tex} \mathrm { ML } ^ { - 1 } \mathrm { T } ^ { - 1 } {/tex}
{tex} \mathrm { MLT } ^ { - 1 } {/tex}
{tex} \mathrm { ML } ^ { - 1 } \mathrm { T } ^ { - 2 } {/tex}
{tex} \mathrm { ML } ^ { - 2 } \mathrm { T } ^ { - 2 } {/tex}
Correct4
Incorrect-1
Out of the following pair, which one does NOT have identical
dimensions is
impulse and momentum
angular momentum and planck's constant
work and torque
moment of inertia and moment of a force (towards north-west)
Correct4
Incorrect-1
The dimension of magnetic field in {tex} \mathrm { M } , \mathrm { L } , \mathrm { T } {/tex} and {tex} \mathrm { C } {/tex} (coulomb)
is given as
{tex} \mathrm { MLT } ^ { - 1 } \mathrm { C } ^ { - 1 } {/tex}
{tex} \mathrm { MT } ^ { 2 } \mathrm { C } ^ { - 2 } {/tex}
{tex} \mathrm { MT } ^ { - 1 } \mathrm { C } ^ { - 1 } {/tex}
{tex} \mathrm { MT } ^ { - 2 } \mathrm { C } ^ { - 1 } {/tex}
Correct4
Incorrect-1
A body of mass {tex} m = 3.513 \mathrm { kg } {/tex} is moving along the x-axis with a speed of {tex} 5.00 \mathrm { ms } ^ { - 1 } . {/tex} The magnitude of its momentum is recorded as
{tex}17.6 \ \mathrm { kg } \mathrm { ms } ^ { - 1 } {/tex}
{tex}17.565\ \mathrm { kg } \mathrm { ms } ^ { - 1 } {/tex}
{tex}17.56\ \mathrm { kg } \mathrm { ms } ^ { - 1 } {/tex}
{tex}17.57\ \mathrm { kg } \mathrm { ms } ^ { - 1 } {/tex}
Correct4
Incorrect-1
Two full turns of the circular scale of a screw gauge cover a distance of {tex}1\, \mathrm { mm } {/tex} on its main scale. The total number of divisions on the circular scale is {tex} 50 . {/tex} Further, it is found that the screw gauge has a zero error of {tex} - 0.03 \mathrm { mm } . {/tex} While measuring the diameter of a thin wire, a student notes the main scale reading of {tex} 3\,\mathrm { mm } {/tex} and the number of circular scale divisions in line with the main scale as {tex} 35 . {/tex} The diameter of the wire is
{tex}3.32\, \mathrm { mm } {/tex}
{tex}3.73\, \mathrm { mm } {/tex}
{tex}3.67\, \mathrm { mm } {/tex}
{tex}3.38\, \mathrm { mm } {/tex}
Correct4
Incorrect-1
In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half- a degree {tex} \left( = 0.5 ^ { \circ } \right) , {/tex} then the least count of the instrument is :
half minute
one degree
half degree
one minute
Correct4
Incorrect-1
The respective number of significant figures for the numbers {tex} 23.023,0.0003 {/tex} and {tex} 2.1 \times 10 ^ { - 3 } {/tex} are
{tex} 5,1,2 {/tex}
{tex} 5,1,5 {/tex}
{tex} 5,5,2 {/tex}
{tex} 4,4,2 {/tex}
Correct4
Incorrect-1
A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading: {tex}0\, \mathrm { mm } {/tex}
Circular scale reading {tex} : 52 {/tex} divisions
Given that 1{tex} \mathrm { mm } {/tex} on main scale corresponds to {tex}100{/tex} divisions of the circular scale. The diameter of wire from the above data is:
{tex}0.052\, \mathrm { cm } {/tex}
{tex}0.026\, \mathrm { cm } {/tex}
{tex}0.005\, \mathrm { cm } {/tex}
{tex}0.52\, \mathrm { cm } {/tex}
Correct4
Incorrect-1
Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3{tex} \% {/tex} each, then error in the value of resistance of the wire is:
6{tex} \% {/tex}
zero
1{tex} \% {/tex}
3{tex} \% {/tex}
Correct4
Incorrect-1
A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the Vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data:
58.59 degree
58.77 degree
58.65 degree
59 degree
Correct4
Incorrect-1
Let {tex} \left[ \epsilon _ { 0 } \right] {/tex} denote the dimensional formula of the permittivity of vacuum. If {tex} \mathrm { M } = {/tex} mass, {tex} \mathrm { L } = {/tex} length, {tex} \mathrm { T } = {/tex} time and {tex} \mathrm { A } = {/tex} electric current, then:
{tex} \epsilon _ { 0 } = \left[ \mathbf { M } ^ { - 1 } \mathbf { L } ^ { - 3 } \mathbf { T } ^ { 2 } \mathbf { A } \right] {/tex}
{tex} \epsilon _ { 0 } = \left[ \mathbf {M} ^ { 1 }\mathbf { L} ^ { 3 }\mathbf { T} ^ { 5 }\mathbf { A} ^ { 2 } \right] {/tex}
{tex} \epsilon _ { 0 } = \left[ \mathbf { M } ^ { 1 } \mathbf { L } ^ { 2 } \mathbf { T } ^ { 1 } \mathbf { A } ^ { 2 } \right] {/tex}
{tex} \epsilon _ { 0 } = \left[ \mathbf { M } ^ { 1 } \mathbf { L } ^ { 2 } \mathbf { T } ^ { 1 } \mathbf { A } \right] {/tex}
Correct4
Incorrect-1
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?
A meter scale.
A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale and main scale has 10 divisions in 1 cm.
A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.
A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.
Correct4
Incorrect-1
The period of oscillation of a simple pendulum is {tex} \mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { \mathrm { g } } } {/tex}
Measured value of {tex} L {/tex} is {tex}20.0 \mathrm { cm } {/tex} known to {tex}1 \mathrm { mm } {/tex} accuracy and time for 100 oscillations of the pendulum is found to be {tex}90 \mathrm { s } {/tex} s using a wrist watch of {tex}1 \mathrm { s } {/tex} resolution. The accuracy in the determination of {tex} \mathrm { g } {/tex} is :
1{tex} \% {/tex}
5{tex} \% {/tex}
2{tex} \% {/tex}
3{tex} \% {/tex}
Correct4
Incorrect-1
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is {tex} 90 \mathrm { s } , 91 \mathrm { s } , 95 \mathrm { s } {/tex} , and {tex} 92 \mathrm { s } {/tex} . If the minimum division in the measuring clock is {tex} 1 \mathrm { s } , {/tex} then the reported mean time should be:
{tex} 92 \pm 1.8 s {/tex}
{tex} 92 \pm 3 s {/tex}
{tex} 92 \pm 2 s {/tex}
{tex} 92 \pm 5.0 \mathrm { s } {/tex}
Correct4
Incorrect-1
A screw gauge with a pitch of {tex}0.5 \mathrm { mm } {/tex} and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the {tex} 45 ^ { \text {th } } {/tex} division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is {tex}0.5 \mathrm { mm } {/tex} and the 25 th division coincides with the main scale line?
{tex}0.70 \mathrm { mm } {/tex}
{tex}0.50\, \mathrm { mm } {/tex}
{tex}0.75\, \mathrm { mm } {/tex}
{tex}0.80\, \mathrm { mm } {/tex}
Correct4
Incorrect-1
Identify the pair whose dimensions are equal.
torque and work
stress and energy
force and stress
force and work.
Correct4
Incorrect-1
Dimensions of {tex} \frac { 1 } { \mu _ { 0 } \varepsilon _ { 0 } } , {/tex} where symbols have their usual meaning, are
{tex} \left[ \mathrm { L } ^ { - 1 } \mathrm { T } \right] {/tex}
{tex} \left[ \mathrm { L } ^ { - 2 } \mathrm { T } ^ { 2 } \right] {/tex}
{tex} \left[ \mathrm { L } ^ { 2 } \mathrm { T } ^ { - 2 } \right] {/tex}
{tex} \left[ \mathrm { LT } ^ { - 1 } \right] {/tex}
Correct4
Incorrect-1
The physical quantities not having same dimensions are
torque and work
momentum and Planck's constant
stress and Young's modulus
speed and {tex} \left( \mu _ { 0 } \varepsilon _ { 0 } \right) ^ { - 1 / 2 } {/tex}
Correct4
Incorrect-1
Which one of the following represents the correct dimensions of the coefficient of viscosity?
{tex} \mathrm { ML } ^ { - 1 } \mathrm { T } ^ { - 2 } {/tex}
{tex} \mathrm { MLT } ^ { - 1 } {/tex}
{tex} \mathrm { ML } ^ { - 1 } \mathrm { T } ^ { - 1 } {/tex}
{tex} \mathrm { M } \mathrm { L } ^ { - 2 } \mathrm { T } ^ { - 2 } {/tex}
Correct4
Incorrect-1
Out of the following pairs which one does not have identical dimensions is
moment of inertia and moment of a force
work and torque
angular momentum and Planck's constant
impulse and momentum
Correct4
Incorrect-1
Which of the following units denotes the dimensions {tex} \mathrm { ML } ^ { 2 } / \mathrm { Q } ^ { 2 } , {/tex} where {tex} \mathrm { Q } {/tex} denotes the electric charge?
weber (Wb)
{tex} \mathrm { Wb } / \mathrm { m } ^ { 2 } {/tex}
henry (H)
{tex} \mathrm { H } / \mathrm { m } ^ { 2 } {/tex}
