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# 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. $$\left[M^2L^2T^{-1}Q\right]$$

Subtopic: Â Dimensions |
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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. $${\left[M^0 L T\right]}$$

Subtopic: Â Dimensions |
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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. $$m=2,~n=2$$

Subtopic: Â Dimensions |
Â 76%
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The period of oscillation of a simple pendulum is given by $$T = 2\pi \sqrt{\frac{l}{g}}$$ where $$l$$ is about $$100~\text{cm}$$ and is known to have $$1~\text{mm}$$ accuracy. The period is about $$2~\text{s}$$. The time of $$100$$ oscillations is measured by a stopwatch of least count $$0.1~\text{s}$$. The percentage error in $$g$$ is:
1. $$0.1\%$$
2. $$1\%$$
3. $$0.2\%$$
4. $$0.8\%$$

Subtopic: Â Errors |
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The percentage errors in the measurement of mass and speed are $$2\%$$ and $$3\%$$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed:
1. $$11\%$$
2. $$8\%$$
3. $$5\%$$
4. $$1\%$$

Subtopic: Â Errors |
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What is the number of significant figures in $$0.310\times 10^{3}?$$
1. $$2$$
2. $$3$$
3. $$4$$
4. $$6$$

Subtopic: Â Significant Figures |
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The decimal equivalent of $$\frac{1}{20}$$ up to three significant figures is:

 1 $$0.0500$$ 2 $$0.05000$$ 3 $$0.0050$$ 4 $$5.0 \times 10^{-2}$$
Subtopic: Â Significant Figures |
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The periods of oscillation of a simple pendulum in an experiment are recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s, and 2.80 s respectively. The average absolute error will be:

1. 0.1 s

2. 0.11 s

3. 0.01 s

4. 1.0 s

Subtopic: Â Errors |
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The length of a cylinder is measured with a meter rod having the least count of $$0.1~\text{cm}$$. Its diameter is measured with vernier callipers having the least count of $$0.01~\text{cm}$$. Given that the length is $$5.0~\text{cm}$$ and the radius is $$2.0~\text{cm}$$. The percentage error in the calculated value of the volume will be:
1. $$1\%$$
2. $$2\%$$
3. $$3\%$$
4. $$4\%$$

Subtopic: Â Errors |
Â 62%
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In an experiment, the following observations were recorded: initial length $$L =2.820~\text{m}$$, mass $$M = 3.00~\text{kg}$$, change in length $$l = 0.087~\text{cm}$$, diameter $$D = 0.041~\text{cm}$$. Taking $$g = 9.81~\text{m/s}^2$$ and using the formula, $$Y = \frac{4MgL}{\pi D^2l},$$ the maximum permissible error in $$Y$$ will be:
1. $$7.96\%$$
2. $$4.56\%$$
3. $$6.50\%$$
4. $$8.42\%$$

Subtopic: Â Errors |
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