Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

(a)

\({{\sqrt{hG}}\over{{c}^{{{3}\over{2}}}}}\)

(b)

\({{\sqrt{hG}}\over{{c}^{{{5}\over{2}}}}}\)

(c)

\(\sqrt{{{hc}\over{G}}}\)

(d)

\(\sqrt{{{Gc}\over{{h}^{{{3}\over{2}}}}}}\)

If a circle with 10 m radius and angle 60° at centre, then what will be the length of arc?

(a)

5.24 m

(b)

6.21 m

(c)

7.1 mm

(d)

10 m

___________ system of units was accepted by the scientists of the general conference on weights and measures.

(a)

FPS

(b)

CGS

(c)

MKS

(d)

SI

One degree of arc is equal to_______

(a)

1.457\(\times\)10²rad

(b)

1.457\(\times\)10^-2rad

(c)

1.745\(\times\)10²rad

(d)

1.745\(\times\)10^-2rad

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate by using the formula p =\(F\over l^2\) .If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is _________________

(a)

1%

(b)

2%

(c)

8%

(d)

10%

A projectile has initially the same horizontal component of velocity as it would acquire if it had moved from rest with uniform acceleration 1 ms^-2? for half a minute. If it reaches the maximum height of 90 m, the angle of, projection is (g =10 ms^-2).

(a)

tan -1\(({1\over \sqrt{5}})\)

(b)

tan ^-1\(({1\over \sqrt{2}})\)

(c)

tan -1\(({1\over \sqrt{3}})\)

(d)

tan -1\(({ \sqrt{2}})\)

An object is dropped from rest. Its v - t graph is ______________.

(a)

(b)

(c)

(d)

When a horse pulls a wagon, the force that causes the horse to move forward is the force?

(a)

the ground exerts on him

(b)

the exerts on the ground

(c)

the wagon exerts on him

(d)

the exerts on the wagon

Which of the following force tends to stopthe moving object?

(a)

Frictional force

(b)

Magnetic force

(c)

Gravitational force

(d)

Electric force

Which one of the following motions on a smooth plane surface does not involve force?

(a)

accelerated motion in a straight line

(b)

retarded motion is a straight line

(c)

motion with constant momentum along a straight line

(d)

motion along a straight line with varying velocity

A jet engine works on the principle of ______________.

(a)

conservation of linear momentum

(b)

conservation of mass

(c)

conservation of energy

(d)

conservation of angular momentum

Which of the following is the dimension of coefficient of friction?

(a)

[MLT^-2]

(b)

[M⁰L⁰T⁰]

(c)

[M²LT^-2]

(d)

[M²LT]

Rate of change of momentum of an object is equal to _______________.

(a)

acceleration

(b)

work done

(c)

force

(d)

impulse

If the potential energy of the particle is \(\alpha -\frac { \beta }{ 2 } { x }^{ 2 }\), then force experienced by the particle is

(a)

F = \(\frac { \beta }{ 2 } { x }^{ 2 }\)

(b)

F = βx

(c)

F = -βx

(d)

F = -\(\frac { \beta }{ 2 } { x }^{ 2 }\)

Two equal masses m₁ and m₂ are moving along the same straight line with velocities 5ms^-1 and -9 ms^-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m₁ and m₂ respectively

(a)

-4 ms^-1 and 10 ms^-1

(b)

10 ms^-1 and 0 ms^-1

(c)

-9 ms^-1 and 5 ms^-1

(d)

5 ms^-1 and 1 ms^-1

Water stored in a dam possesses _______________.

(a)

no energy

(b)

electrical energy

(c)

kinetic energy

(d)

potential energy

A shell, in flight explodes into four unequal parts. Which is conserved?

(a)

potential energy

(b)

momentum

(c)

kinetic energy

(d)

both a and c

Unit of work is ____________.

(a)

watt

(b)

newton

(c)

joule

(d)

no unit

A particle is dropped from a height h. A constant horizontal velocity is given to the particle. Taking g to be constant everywhere, kinetic energy E of the particle with respect to time z is correctly shown in ____________.

(a)

(b)

(c)

(d)

In an explosion, a body breaks up into two pieces of unequal masses. In this ____________.

(a)

both parts will have numerically equal momentum

(b)

lighter part will have more momentum

(c)

heavier part will have more momentum

(d)

both parts will have equal kinetic energy

A long spring when stretched by 2 cm its potential energy is U. If the spring is stretched by 10 cm. then the potential energy of the spring is _______________.

(a)

\(\frac{U}{5}\)

(b)

5U

(c)

\(\frac{U}{25}\)

(d)

25U

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be ____________.

(a)

2Mg/k

(b)

4Mg/k

(c)

Mg/2k

(d)

Mg/k

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

Two bodies with kinetic energies in the ratio of 4: 1 are moving with equal linear momentum. The ratio of their masses is _______________.

(a)

4: 1

(b)

1:1

(c)

1:2

(d)

1:4

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

(a)

a line perpendicular to the plane of rotation

(b)

the line making an angle of 45^o to the plane of rotation

(c)

the radius

(d)

tangent to the path