Which relation is wrong?

(a)

1 fermi = 10^-14 m

(b)

r nanometer = 10^-9 m

(c)

1 AU = 1.496 X 10¹¹ m

(d)

1 parsec = 3.26 light year

Two quantities A and B have different dimensions which mathematical operation given below is physically meaningful?

(a)

A/B

(b)

A+B

(c)

A-B

(d)

A=B

The ratio of one nanometer to one micron is__________________

(a)

10^-3

(b)

10³

(c)

10^-9

(d)

10^-6

Zero error of an instrument is a______________.

(a)

Systematic error

(b)

Random error

(c)

Gross error

(d)

Both (a) and (b)

Dimensions [M L^-1T^-1] are related to_____________

(a)

torque

(b)

work

(c)

energy

(d)

Coefficient of viscosity

If a particle has negative velocity and negative acceleration, its speed

(a)

increases

(b)

decreases

(c)

remains same

(d)

zero

Consider the quantities pressure, power, energy, impulse, charge. Out of these, the only vector quantity is _______________.

(a)

pressure

(b)

power

(c)

impulse

(d)

charge

If the length of the second hand in a stop clock is 3cm. The angular velocity and linear velocity of the tip is _______________

(a)

0.2047 rad/s; 0.0314 ms^-1

(b)

0.2547 rad/s; 0.314 ms^-1

(c)

0.1472 rad/s; 0.06314 ms^-1

(d)

0.1047 rad/s; 0.00314 ms^-1

The speed of a train is reduced from 60 kmh^-1 to 15 kmh^-1 in a distance of 450 m. If the retardation is uniform is the distance, it will travel further before coming to rest is _______________.

(a)

25m

(b)

30m

(c)

15m

(d)

20m

The radius of the earth was measured by _____________.

(a)

Newton

(b)

Eratosthenes

(c)

Galileo

(d)

Ptolemy

Which of the following is not a scalar?

(a)

Volume

(b)

angular momentum

(c)

Relative density

(d)

time

If the radii of circular paths of two particles of same masses are in the ratio 2 : 3 then to have a constant centripetal force, their velocities should be in a ratio of _____________.

(a)

\(1:\sqrt { 2 } \)

(b)

\(\sqrt { 2 } :\sqrt { 3 } \)

(c)

\(\sqrt { 3 } :\sqrt { 2 } \)

(d)

1:\(\sqrt { 3 } \)

The unit of co-efficient of static friction is _____________.

(a)

N

(b)

Mn

(c)

Ns

(d)

no unit

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

(a)

\(\frac{2}{3}\)k

(b)

\(\frac{3}{2}\)k

(c)

3k

(d)

6k

Same retarding force is applied to stop the train in certain distance. When the speed is doubled, how is this distance changed?

(a)

Remain same

(b)

Gets doubled

(c)

Gets doubled

(d)

Gets four times

A stationary particle explodes into two particles of masses m₁ and m₂, which move in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁/E₂ is ______________

(a)

m₂/m₁

(b)

m₁/m₂

(c)

1

(d)

m₁v₂/m₂v₁

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia

(a)

increases

(b)

decreases

(c)

remains constant

(d)

depends on direction of rotation

Which of the following has largest M.I _________________.

(a)

Ring about its axis perpendicular to its plane

(b)

Disc about its axis perpendicular to its plane

(c)

Solid sphere

(d)

Bar magnet

When a steady torque is acting on a body, the body _________________

(a)

continues in its state of rest or uniform motion along a straight line

(b)

gets linear acceleration

(c)

gets angular acceleration

(d)

rotates at a constant speed

The moment of inertia of a body about a given axis is 1.2 kgm². Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration 25 radian/sec² must be applied about that axis lor a duration of ____________.

(a)

4 s

(b)

2 s

(c)

8 s

(d)

10 s

The positions of two masses m₁ and m₂ are x₁ and x₂. The position of center of mass is _____________.

(a)

\(\frac{m_1m_2}{m_1x_1+m_2x_2}\)

(b)

\(m_1x_1+m_2x_2\)

(c)

\(\frac{m_1x_1+m_2x_2}{m_1+m_2}\)

(d)

\(\frac{m(x_1+x_2)}{m_1+m_2}\)

The gravitational potential energy of the Moon with respect to Earth is

(a)

always positive

(b)

always negative

(c)

can be positive or negative

(d)

always zero

In a streamline flow ______________.

(a)

the speed ofa particle always remain same

(b)

the velocity of a particle always remains same

(c)

the kinetic energies of all the particles arriving at a given point at the same

(d)

the moments of the particles arriving at a given point are different

A raindrop falls near the surface of the earth with almost uniform velocity because _____________.

(a)

its weight is negligible

(b)

the force of surface tension balances its weight

(c)

the force of viscosity of air balances its weight

(d)

the drops are charged and atmospheric electric field balances its weight

If the temperature of the wire is increased, then the Young’s modulus will 

(a)

remain the same

(b)

decrease

(c)

increase rapidly

(d)

increase by very a small amount