A physical quantity A is related to four observables a, b, c and d as follows :

$\mathrm{A} = \frac{{\mathrm{a}}^2{\mathrm{b}}^3}{\mathrm{c}\sqrt{\mathrm{d}}}$ . The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A ?

• 12 %

• 7 %

• 5 %

• 14 %

102.

The velocity of a particle v at an instant t is given by v = at + bt²  the dimension of b is 

• [L]

• [LT^-1]

• [LT^-2]

• [LT^-3]

The dimension of angular momentum is

• [M⁰L¹T^-1]

• [M¹L²T^-2]

• [M¹L²T¹]

• [M²L¹T^-2]

In a slide caliper, (m + 1) number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is

• d / (m + 1) unit

• d / m unit

• md / (m + 1) unit

• (m + 1)d / m unit

In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows

$\mathrm{P} = \frac{{\mathrm{a}}^3{\mathrm{b}}^2}{\mathrm{cd}} \%$, Error in P is 

• 14 %

• 10 %

• 7 %

• 4 %

In which of the following pairs, the two physical quantities have different dimensions ?

• Planck's constant and angular momentum

• Impulse and linear momentum

• Moment of inertia and moment of a force

• Energy and torque

If n denotes a positive integer, h the Planck's constant, q the charge and B the magnetic field, then the quantity $\left[\frac{\mathrm{nh}}{2\mathrm{\pi qB}}\right]$ has the dimension of

• area

• length

• speed

• acceleration