A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate \(g,\) the acceleration due to gravity. If the maximum percentage errors in the measurement of the distance and the time are \(e_1\) and \(e_2\) respectively, the percentage error in the estimation of \(g\) is:
1.
2.
3.
4.
The density of a material in a CGS system of units is \(4~\text{grams/cm}^3\). In a system of units in which the unit of length is \(10~\text{cm}\) and the unit of mass is \(100~\text{grams}\), the value of the density of the material will be:
1. \( 0.04 \)
2. \( 0.4 \)
3. \( 40 \)
4. \(400\)
1. | impulse and surface tension |
2. | angular momentum and work |
3. | work and torque |
4. | Young's modulus and energy |
The velocity \(v\) of a particle at time \(t\) is given by \(v=at+\dfrac{b}{t+c}\), where \(a,\) \(b\) and \(c\) are constants. The dimensions of \(a,\) \(b\) and \(c\) are respectively:
1. \(\left[{LT}^{-2}\right],[{L}] \text { and }[{T}]\)
2. \( {\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]} \)
3. \( {\left[{LT}^2\right],[{LT}] \text { and }[{L}]} \)
4. \( {[{L}],[{LT}] \text { and }\left[{T}^2\right]}\)
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T, and current I, would be:
1.
2.
3.
4.
Which two of the following five physical parameters have the same dimensions?
(1) | Energy density |
(2) | Refractive index |
(3) | Dielectric constant |
(4) | Young's modulus |
(5) | Magnetic field |
Choose the correct option:
1. | (2) and (4) |
2. | (3) and (5) |
3. | (1) and (4) |
4. | (1) and (5) |
If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:
1. 4%
2. 6%
3. 8%
4. 2%
1. | \(a=1,\) \(b=-1,\) \(c=-2\) | pressure if
2. | \(a=1,\) \(b=0,\) \(c=-1\) | velocity if
3. | \(a=1,\) \(b=1,\) \(c=-2\) | acceleration if
4. | \(a=0,\) \(b=-1,\) \(c=-2\) | force if
The dimensions of where is the permittivity of free space and E is the electric field, are:
1. [ML2T-2]
2. [ML-1T-2]
3. [ML2T-1]
4. [MLT-1]