Addition & Subtraction of Errors

Q. The volume of two bodies are measured to be $V_1=(10.20\pm 0.02){\text{cm}}^3$ and $V_2=(6.40\pm 0.01){\text{cm}}^3$.
The difference in volume with appropriate significant figures is

1. $(3.80\pm 0.04){\text{cm}}^3$
2. $(3.80\pm 0.01){\text{cm}}^3$
3. $(3.80\pm 0.03){\text{cm}}^3$
4. $(3.80\pm 0.02){\text{cm}}^3$

Q. If the length of the rod $A$ is $(3.25\pm 0.01)\text{cm}$ and that of the rod $B$ is $(4.19\pm 0.01)\text{cm}$ then the rod $B$ is longer than rod $A$ by

1. $(0.94\pm 0.03)\text{cm}$
2. $(0.94\pm 0.01)\text{cm}$
3. $(0.94\pm 0.02)\text{cm}$
4. $(0.94\pm 0.04)\text{cm}$

Q. How is random error eliminated or minimised?

1. By choosing accurate equipments
2. By applying better methods of readings
3. By taking more number of observations
4. By selecting better techniques

Q. The volume of two bodies are measured to be $V_1=(10.20\pm 0.02){\text{cm}}^3$ and $V_2=(6.40\pm 0.01){\text{cm}}^3$.
The difference in volume with appropriate significant figures is

1. $(3.80\pm 0.04){\text{cm}}^3$
2. $(3.80\pm 0.01){\text{cm}}^3$
3. $(3.80\pm 0.03){\text{cm}}^3$
4. $(3.80\pm 0.02){\text{cm}}^3$

Q.

The mass of Mr x is 50kg and the uncertainty in measurement is 1 kg.The mass of Mr y is 55kg and the uncertainty in measurement is 2 kg. Find the difference of their masses with correct uncertainties.

1. 105 $\pm$ 3 kg

2. 5 $\pm$ 1 kg

3. 5 $\pm$ 3 kg

4. None of these

Q. While actual errors only get added, relative errors may get subtracted at times.

1. False
2. True

Q. If the length of the rod $A$ is $(3.25\pm 0.01)\text{cm}$ and that of the rod $B$ is $(4.19\pm 0.01)\text{cm}$ then the rod $B$ is longer than rod $A$ by

1. $(0.94\pm 0.03)\text{cm}$
2. $(0.94\pm 0.01)\text{cm}$
3. $(0.94\pm 0.02)\text{cm}$
4. $(0.94\pm 0.04)\text{cm}$

Q. A physical quantity $x$ is represented as $x=M^2{L}^3{T}^{-1}$, and maximum percentage errors in $M,L$ & $T$ are 1%, 2% and 1% respectively, then maximum percentage error in $x$ is

1. 7%
2. 8%
3. 9%
4. 5%

Q. If the length of the rod $A$ is $(3.25\pm 0.01)\text{cm}$ and that of the rod $B$ is $(4.19\pm 0.01)\text{cm}$ then the rod $B$ is longer than rod $A$ by

1. $(0.94\pm 0.03)\text{cm}$
2. $(0.94\pm 0.01)\text{cm}$
3. $(0.94\pm 0.02)\text{cm}$
4. $(0.94\pm 0.04)\text{cm}$

Q. A physical quantity $x$ is represented as $x=M^2{L}^3{T}^{-1}$, and maximum percentage errors in $M,L$ & $T$ are 1%, 2% and 1% respectively, then maximum percentage error in $x$ is

1. 7%
2. 8%
3. 9%
4. 5%

Q. Weighing machine ${}^{\prime }{A}^{\prime }$ is showing 15.324 kg, and weighing machine ${}^{\prime }{B}^{\prime }$ is showing 15.1 kg for an object whose actual mass is 15 kg then,

1. ${}^{\prime }{A}^{\prime }$ is more precise but less accurate than ${}^{\prime }{B}^{\prime }$.
2. ${}^{\prime }{A}^{\prime }$ is less precise but more accurate than ${}^{\prime }{B}^{\prime }$.
3. ${}^{\prime }{A}^{\prime }$ is more precise and more accurate than ${}^{\prime }{B}^{\prime }$.
4. ${}^{\prime }{B}^{\prime }$ is more precise and more accurate than ${}^{\prime }{A}^{\prime }$.

Q. A physical quantity $x$ is represented as $x=M^2{L}^3{T}^{-1}$, and maximum percentage errors in $M,L$ & $T$ are 1%, 2% and 1% respectively, then maximum percentage error in $x$ is

1. 7%
2. 8%
3. 9%
4. 5%

Q. A physical quantity $x$ is represented as $x=M^2{L}^3{T}^{-1}$, and maximum percentage errors in $M,L$ & $T$ are 1%, 2% and 1% respectively, then maximum percentage error in $x$ is

1. 7%
2. 8%
3. 9%
4. 5%