11.

The distance between the centres of carbon and oxygen atoms in the carbon monoxide molecule is 1.130 $\stackrel{\circ }{\mathrm{A}}$. Locate the centre of mass of the molecule relative to the carbon atom

• $5.428 \stackrel{\circ }{\mathrm{A}}$

• $1.130 \stackrel{\circ }{\mathrm{A}}$

• $0.6457 \stackrel{\circ }{\mathrm{A}}$

• $0.3260 \stackrel{\circ }{\mathrm{A}}$

Which of the following sets of quantities have same dimensional formula ?

• Frequency, angular frequency and angular momentum

• Surface tension, stress and spring constant

• Work, energy and torque

• Thermal capacity, specific heat and entropy

A 20 kg ball moving with a velocity 6 m/s collides with a 30 kg ball initially at rest. If both of them coalesce, then the final velocity of the combined mass is

• 6 m/s

• 5 m/s

• 3.6 m/s

• 2.4 m/s

A monkey climbs up and another monkey climbs down a rope hanging from a tree with same uniform acceleration separately. If the respective masses of monkeys are in the ratio 2 : 3, the common acceleration must be

• g/5

• 6g

• g/2

• g

A running man has the same kinetic energy as that of a boy of half his mass. The man speeds up by 2 ms^-1 and the boy changes his speed by x ms^-1, so that the kinetic energies of the boy and the man are again equal. Then x in ms^-1 is

• $- 2\sqrt{2}$

• $+ 2\sqrt{2}$

• $\sqrt{2}$

• 2

Two cars A and B are travelling in the same direction with velocities v₁ and v₂ (v₁ > v₂). When the car A is at a distance d behind the car B, the driver of the car A applies the brake producing uniform retardation, a. There will be no collision when

• $\mathrm{d} < \left(\frac{{\mathrm{v}}_1 - {\mathrm{v}}_2}{2\mathrm{a}}\right)$

• $\mathrm{d} > \frac{{{\mathrm{v}}_1}^2 - {{\mathrm{v}}_2}^2}{2\mathrm{a}}$

• $\mathrm{d} > \frac{{\left({\mathrm{v}}_1 - {\mathrm{v}}_2\right)}^2}{2\mathrm{a}}$

• $\mathrm{d} < \frac{{{\mathrm{v}}_1}^2 - {{\mathrm{v}}_2}^2}{2\mathrm{a}}$

A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 1 kgm² and its rate of rotation 2 rev/s. The angular momentum is

• 1.257 kg m²/s

• 12.57 kg m²/s

• 13.57 kg m²/s

• 20 kg m²/s

A car of mass 1000 kg moves on a circular track of radius 20 m. If the coefficient of friction is 0.64, then the maximum velocity with which the car can move is

• 15 m/s

• 11.2 m/s

• 20 m/s

• 18 m/s

Two planets have radii r₁ and r₂ and densities d₁ and d₂ respectvely. Then the ratio of acceleration due to gravity on them will be

• r₁d₁ : r₂d₂

• r₁d₂ : r₂d₁

• r₁²d₁ : r₂²d₂

• r₁ : r₂

A physical quantity P is related to four measurable quantities a, b, c and d as follows

         $\mathrm{P} = \frac{{\mathrm{a}}^3{\mathrm{b}}^2}{\sqrt{\mathrm{c}}\mathrm{d}}$

The percentage errors of measurement in a, b, c and d are 1 %, 3% ,4% and 2%. The percentage error in the quantity P is

• 10 %

• 13 %

• 5 %

• 15 %