The physical quantity having dimensions [M^-1L^-3T³A²] is

• resistance

• resistivity

• electrical conductivity

• electromotive force

If the coefficient of static friction between the tyres and road is 0.5, what is the shortest distance in which an automobile can be stopped when travelling at 72 kmh^-1 ?

• 50 m

• 60 m

• 40.8 m

• 80.16 m

The upper half of an inclined plane with inclination $\mathrm{\varphi }$ is perfectly smooth, while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the lower half is given by

• 2 sin $\mathrm{\varphi }$

• 2 cos $\mathrm{\varphi }$

• 2 tan $\mathrm{\varphi }$

• tan $\mathrm{\varphi }$

What is the property of two vectors A and B, if$\left|\mathrm{A} + \mathrm{B}\right| = \left|\mathrm{A} - \mathrm{B}\right|$

• A and B are parallel to each other

• A and B are perpendicular to each other

• A and B are antiparallel to each other

• A and B are unit vectors

A disc revolves with a speed of $33\frac{1}{3}$ rev min^-1 and a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the disc. If coefficient of friction between the coins and the disc is 0.15, then which of the two coins will revolve with the disc?

• coin placed at a distance 4 cm

• coin placed at a distance 14 cm

• both coins

• Neither one of the coins

A heavy particle hanging from a fixed point by a light inextensible string of length l is projected horizontally with speed $\sqrt{\mathrm{gl}}$. When the tension in the string is equal to the weight of the particle, then the speed of particles and the inclination of the string to the vertical at the instant of motion are

• $\sqrt{\frac{\mathrm{gl}}{2}} , {\cos }^{-1}\left(\frac{1}{2}\right)$

• $\sqrt{\mathrm{gl}} , {\cos }^{-1}\left(\frac{3}{2}\right)$

• $\sqrt{\frac{\mathrm{gl}}{3}} , {\cos }^{-1} \left(\frac{2}{3}\right)$

• $\sqrt{\mathrm{gl}} , {\cos }^{-1} \left(\frac{2}{3}\right)$

A uniform sphere of mass 500 g rolls down a plane surface without slipping on it, so that its centre moves at a speed of 0.02ms^-1 . The total kinetic energy of rolling sphere would be (in J)

• 1.4 × 10^-4 J

• 0.75 × 10^-3 J

• 5.75 × 10^-3 J

• 4.9 × 10^-5 J

If a thin uniform wire of length X having linear mass density D is bent zero into a circular loop (as shown in the figure). What will be the moment of inertia of the loop about axis AB ?

• 3 L²D/ 16 $\mathrm{\pi }$

• 2 L²D/ 3$\mathrm{\pi }$

• 3 L³D/ 8${\mathrm{\pi }}^2$

• 8 L²D/ 13${\mathrm{\pi }}^2$

A toy rocket of mass 0.1 kg has a small fuel of mass 0.02 kg, which it burns out in 3s. Starting from rest on a horizontal smooth track, it get a speed of 20 ms^-1 after the fuel is burn out. The energy content per unit mass of the fuel is (Ignore the small mass variation of the rocket during fuel burning)

• 20 J/kg

• 100 J/Kg

• 1000 J/kg

• 400 J/kg

A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle xyz with its vertices on the perimeter of disc. After one second applying the forces, the angular speed of the disc in rad/s is

• 4

• 2

• 6

• 8