Multiplication & Division of Errors

Q. A physical quantity P is related to four observables a, b, c and d as follows : P = a³ b ²/ (√c d) The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?

Q.

The fractional change in the value of free-fall acceleration g for a particle when it is lifted from the surface to an elevation h (h<<R) is

1. 

2. 

3. 

4. None of these

Q. If radius of the sphere is (5.3 $\pm$ 0.1)cm. Then percentage error in its volume will be

1. 3+6.01 $\times \frac{100}{5.3}$
2. $\frac{1}{3}\times$ 0.01 $\times \frac{100}{5.3}$
3. $\left(\frac{3\times 0.1}{5.3}\right)\times 100$
4. $\frac{0.1}{5.3}\times 100$

Q. Distance covered by particle is 200.0 $\pm$ 0.4 m, and time taken to cover it is 18.0 $\pm$ 0.9 s. Percentage error in speed is :

1. 7 %
2. 5.2 %
3. 2.5 %
4. 14 %

Q. Assertion $\left(A\right)$: Absolute error in physical quantity can be positive, negative or zero.
Reason $\left(R\right)$: Absolute error is the difference in measured value and true value of physical quantity.
Choose the correct option:

1. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
2. Both $A$ and $R$ are true and $R$ is not the correct explanation of $A$.
3. $A$ is true but $R$ is false.
4. $A$ is false but $R$ is true.

Q. Length $l$ and Acceleration due to gravity $g$ are measured with $\pm 6\%$ and $\pm 4\%$ errors respectively. The percentage error in determination of the Time period of a simple pendulum will be,

1. $\pm 7\%$
2. $\pm 2\%$
3. $\pm 5\%$
4. $\pm 4\%$

Q. The side of a cube is measured by vernier caliper ($10$ divisions of vernier scale coincide with $9$ divisions of main scale, where $1$ division of main scale is $1\text{mm}$). The main scale reads $10\text{mm}$ and the first division of the vernier scale coincides with the main scale. The maximum $\%$ error in measurement of volume of the cube will be

1. $3\%$
2. $5\%$
3. $6\%$
4. $8\%$

Q. The energy of a system as a function of time $t$ is given as $E\left(t\right)=e^{-\alpha t}{A}^2$, where $\alpha =0.2s^{-1}$. The measurement of $A$ has an error of $1.25\%$. If the error in the measurement of time is $1.50\%$, the percentage error in the value of $E\left(t\right)$ at $t=5s\text{is}$
(Approximate your answer in integer value)

Q. The length of cylinder is measured with a metre rod having least count $0.1\text{cm}$. Its diameter is measured with vernier caliper having least count $0.01\text{cm}$. Given that length is $5.0\text{cm}$ and diameter is $4.0\text{cm}$. The percentage error in the calculated value of the volume will be

1. $1.5\%$
2. $2.5\%$
3. $3.5\%$
4. $4\%$

Q. Assertion $\left(A\right)$: Absolute error in physical quantity can be positive, negative or zero.
Reason $\left(R\right)$: Absolute error is the difference in measured value and true value of physical quantity.
Choose the correct option:

1. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
2. Both $A$ and $R$ are true and $R$ is not the correct explanation of $A$.
3. $A$ is true but $R$ is false.
4. $A$ is false but $R$ is true.

Q. If the radius of earth shrinks by $1.5\%$ (mass remaining same), then the value of gravitational accelaration changes by

1. $3\%$
2. $2\%$
3. $-2\%$
4. $-3\%$

Q. In the operation $(x+\Delta x)(y+\Delta y)$, we always ignore $\Delta x\Delta y$.

1. False
2. True

Q.

What is the error in the area of a rectangle?

Given: L=5 $\pm$ 1 units

B= 4$\pm$2 units

1. $\pm -14$

2. $\pm -12$

3. $\pm -16$

4. none of these

Q.

What is the error in the area of a rectangle?

Given: L=5 $\pm$ 1 units

B= 4$\pm$2 units

1. $\pm -14$

2. $\pm -12$

3. $\pm -16$

4. none of these

Q. According to Joule's law of heating, heat produced $H=I^{2}Rt,$ where $I$ is current, $R$ is resistance and $t$ is time. If the errors in the measurements of $I$, $R$ and $t$ are 3%, 4% and 6% respectively, then error in the measurement of H is

1. $\pm 17\%$
2. $\pm 16\%$
3. $\pm 19\%$
4. $\pm 25\%$

Q. The resistance $R=\frac{V}{I}$, where $V=100\pm 5$ volts and $I=10\pm 0.3$ amperes. Calculate the percentage error in $R$.

1. 8 %
2. 10 %
3. 12 %
4. 14 %

Q. According to Joule's law of heating, heat produced $H=I^{2}Rt,$ where $I$ is current, $R$ is resistance and $t$ is time. If the errors in the measurements of $I$, $R$ and $t$ are 3%, 4% and 6% respectively, then error in the measurement of H is

1. $\pm 17\%$
2. $\pm 16\%$
3. $\pm 19\%$
4. $\pm 25\%$

Q. The side of a cube is measured by vernier caliper ($10$ divisions of vernier scale coincide with $9$ divisions of main scale, where $1$ division of main scale is $1\text{mm}$). The main scale reads $10\text{mm}$ and the first division of the vernier scale coincides with the main scale. The maximum $\%$ error in measurement of volume of the cube will be

1. $5\%$
2. $8\%$
3. $3\%$
4. $6\%$

Q. In the operation $(x+\Delta x)(y+\Delta y)$, we always ignore $\Delta x\Delta y$.

1. False
2. True

Q. If radius of the sphere is (5.3 $\pm$ 0.1)cm. Then percentage error in its volume will be

1. 3+6.01 $\times \frac{100}{5.3}$
2. $\frac{1}{3}\times$ 0.01 $\times \frac{100}{5.3}$
3. $\left(\frac{3\times 0.1}{5.3}\right)\times 100$
4. $\frac{0.1}{5.3}\times 100$

Q. The mass and density of a solid sphere are measured to be $(12.4\pm 0.1)\text{kg}$ and $(4.60\pm 0.2){\text{kg/m}}^3$. The volume of the sphere expressed with error limits is:

1. $(15\pm 0.1){\text{m}}^3$
2. $(2.7\pm 0.3){\text{m}}^3$
3. $(14.6\pm 0.2){\text{m}}^3$
4. $(2.69\pm 0.1){\text{m}}^3$

Q. The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is

1. 1%
2. 2%
3. 6%
4. 8%

Q. Assertion $\left(A\right)$: Absolute error in physical quantity can be positive, negative or zero.
Reason $\left(R\right)$: Absolute error is the difference in measured value and true value of physical quantity.
Choose the correct option:

1. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
2. Both $A$ and $R$ are true and $R$ is not the correct explanation of $A$.
3. $A$ is true but $R$ is false.
4. $A$ is false but $R$ is true.

Q. The side of a cube is measured by vernier caliper ($10$ divisions of vernier scale coincide with $9$ divisions of main scale, where $1$ division of main scale is $1\text{mm}$). The main scale reads $10\text{mm}$ and the first division of the vernier scale coincides with the main scale. The maximum $\%$ error in measurement of volume of the cube will be

1. $3\%$
2. $5\%$
3. $6\%$
4. $8\%$