**Uncertainty (error)**

(33) Percentage uncertainty recorded in the measurement of the radius of the sphere is 4%. The uncertainty in the area of the sphere will be

(a) 16% (b)
4% (c) 12% **(d) 8%**

Solution: Surface area of a sphere = 4πr^{2}

%age uncertainty in radius = 4%

By power rule, the %age uncertainty in the value of area of the sphere= 2*4 = 8%

(34) Percentage uncertainty recorded in the measurement of the radius of the sphere is 4%. The uncertainty in the volume of the sphere will be

(a) 16% (b)
4% **(c) 12% ** (d)
8%

Hint: Use power rule.

(35) Percentage uncertainty recorded in the measurement of the radius of the circle is 4%. The uncertainty in the circumference of the circle will be

(a) 16% **(b)
4%** (c) 12% (d) 8%

(Do you know why?)

(36) The density of steel ball was determined by measuring the mass and diameter. The mass was measured with 1% error and diameter 3% of error. Error in the calculated density of the steel ball is at most:

(a) 2% (b)
4% (c) 8% **(d) 10%**

Hint 1: Since radius = diameter/2 . Now 2 is constant, therefore, its percentage error is 0. Applying the quotient rule for finding uncertainty in the division, d/2.

Percent uncertainty in r = Percent uncertainty in diameter + percent uncertainty in 2 = 3+0 = 3

Hint 2: Volume of the sphere is 4/3 π r^{3}. Apply
power rule to find uncertainty in volume.

Hint 3: Density = mass/volume. Apply quotient rule to find uncertainty in density.

(37) Force F is applied on mass m to produce acceleration a. Percentage uncertainty in the measurement of F is 2% and m is 1%. What is the percentage uncertainty in a.

(a) 1% (b)
2% **(c) 3% ** (d)
4%

(38) Percentage uncertainties in the measurements of mass and velocity are 1% and 1.5% respectively. Percentage uncertainty in K.E is

(a) 1% (b)
2% (c) 3% **(d) 4%**

Hint: Percentage uncertainty in v^{2} is 2*1.5 = 3
and percentage uncertainty in mv^{2} = 1+2 = 3

(39) If error in the measurement of mass and length of a cube are 1% and 2% respectively, the maximum error in the measurement of the density of the cube will be

(a) 3% (b)
6% **(c)
7%** (d)
11%

**Solution **density
= mass/volume ——– (A)

Now if l is the length of the cube, then volume of the cube
is l^{3}.

To find error in the volume (note that the given error is in the length of the cube)we apply the power rule of uncertainty. Therefore, percentage uncertainty in the volume is 3*2 = 6

Now using equation (A), we find the uncertainty in density by applying the quotient (division) rule.

Percentage uncertainty in the density = (1+6) = 7

(40) The maximum error in the measurement of mass and length of a cube are 2% and 3% respectively. The maximum error in the measurement of its density will be

(a) 1% (b)
5% (c) 7% **(d) 11%**

**Dimensions**

(41) The dimensions of Plank’s constant are

(a) MLT^{-2} **(b)
ML ^{2}T^{-1}** (c)
MLT

^{-3}(d) ML

^{2}T

^{-2}

(42) The dimensions of gravitational constant are

(a) ML^{2}T^{-2} **(b) M ^{-1}L^{3}T^{-2}** (c) MLT

^{-3}(d) ML

^{-2}T

^{-1}

Hint: Gravitational constant G = W.r^{2}/m_{1}m_{2}

(43) The dimensions of torque are similar to the dimensions of

(a) Force **(b)
Einstein’s Energy Mass equation** (c)
Plank’s Constant (d) Angular
momentum

Solution

Einstein energy mass equation is E = mc^{2} (c is
the velocity of light)

In terms of dimensions mc^{2} = M L T^{-2} ——— (i)

Torque = rFsinθ

In terms of dimensions, rFsinθ = L M T^{-2} ————- (ii)

(Note that sin θ is the ratio of two lengths, therefore, it has no dimensions)

Comparing (i) and (ii) proves the assertion.

(44) Which one of the following is a dimensionless physical quantity?

(a)Gravitational constant **(b)
coefficient of friction** (c)
density (d)
speed

(45) A car is moving with a speed of 72 km/hr. Its speed in proper SI units is

(a) 2 m/hr (b)
22 m/s (c) 0.2
km/s **(d)
20 m/s**

Solution:

**Precision and accuracy**

(46) Speed of sound at 0^{0}C is 332 m/s. A student
measured the speed repeatedly and obtained the values

(1) 330 m/s (2) 329.8 m/s (3) 330.2 m/s (4) 329.75 m/s

His data is

**(a) More precise, less accurate** (b)
More accurate, less precise

(c) Neither precise nor accurate (d) both precise and accurate

(See theory, question on precision and accuracy).

(47) A student measured the speed of sound repeatedly and obtained the data

(1) 333 m/s (2) 332.5 m/s (3) 332 m/s (4) 331.8 m/s

His data is

(a) More precise, less accurate **(b) More
accurate, less precise**

(c) Neither precise nor accurate (d) both precise and accurate

(48) A student measured the speed of sound repeatedly and obtained the data

(1) 335 m/s (2) 330 m/s (3) 329 m/s (4) 325.5 m/s

His data is

(a) More precise, less accurate (b) More accurate, less precise

**(c) Neither precise nor accurate** (d)
both precise and accurate

(49) A student measured the speed of sound repeatedly and obtained the data

(1) 332 m/s (2) 332.3 m/s (3) 332.8 m/s (4) 332.5 m/s

His data is

(a) More precise, less accurate (b) More accurate, less precise

(c) Neither precise nor accurate **(d) both precise
and accurate**