If \(u_1\) and \(u_2\) are the units selected in two systems of measurement and \(n_1\) and \(n_2\) are their numerical values, then:
1. | \(n_1u_1=n_2u_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
2. | \(n_1u_1+n_2u_2=0\) |
3. | \(n_1n_2=u_1u_2\) |
4. | \((n_1+u_1)=(n_2+u_2)\) |
The velocity \(v\) of a particle at time \(t\) is given by \({v}={at}+\frac{{b}}{{t}+{c}}.\) The dimensions of \({a}\), \({b}\), and \({c}\) are respectively:
1. \( {\left[{LT}^{-2}\right],[{L}],[{T}]} \)
2. \( {\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]} \)
3. \( {\left[{LT}^2\right],[{LT}] \text { and }[{L}]} \)
4. \( {[{L}],[{LT}], \text { and }\left[{T}^2\right]}\)
If the dimensions of a physical quantity are given by \([M^aL^bT^c],\)
1. | pressure if \(a=1, ~b=-1,~c=-2\) |
2. | velocity if \(a=1,~b=0,~c=-1\) |
3. | acceleration if \(a=1,~b=1,~c=-2\) |
4. | force if \(a=0, ~b= -1,~c=-2\) |
Dimensions of electric current are:
1. \(\left[M^0L^0T^{-1}Q\right]\)
2. \(\left[M^1L^2T^{-1}Q\right]\)
3. \(\left[M^2L^1T^{-1}Q\right]\)
4. \(\left[M^2L^2T^{-1}Q\right]\)
The position of a body with acceleration \(a\) is given by \(x= Ka^{m}t^{n}\) (assume \(t\) to be time). The values of \(m\) and \(n\) will be:
1. | \(m=1,~n=1\) | 2. | \(m=1,~n=2\) |
3. | \(m=2,~n=1\) | 4. | \(m=2,~n=2\) |
The dimensional formula of pressure is:
1. | \(\left[MLT^{-2}\right]\) | 2. | \(\left[ML^{-1}T^{2}\right]\) |
3. | \(\left[ML^{-1}T^{-2}\right]\) | 4. | \(\left[MLT^{2}\right]\) |
The dimensional formula for impulse is:
1. | \([MLT^{-2}]\) | 2. | \([MLT^{-1}]\) |
3. | \([ML^2T^{-1}]\) | 4. | \([M^2LT^{-1}]\) |
In the relation, \(y=a \cos (\omega t-k x)\), the dimensional formula for \(k\) will be:
1. \( {\left[M^0 L^{-1} T^{-1}\right]} \)
2. \({\left[M^0 L T^{-1}\right]} \)
3. \( {\left[M^0 L^{-1} T^0\right]} \)
4. \({\left[M^0 L T\right]}\)
When units of mass, length, and time are taken as \(10~\text{kg}, 60~\text{m}~\text{and}~60~\text{s}\) respectively, the new unit of energy becomes \(x\) times the initial SI unit of energy. The value of \(x\) will be:
1. \(10\)
2. \(20\)
3. \(60\)
4. \(120\)
If the units of force and length, is increased by four times, then the unit of energy increases by:
1. | 16 times | 2. | 8 times |
3. | 2 times | 4. | 4 times |