The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is: (For steel, Young’s modulus is 2×10^{11} N m^{–2} and coefficient of thermal expansion is 1.1×10^{-5} K^{-1})

- 2.2 × 10
^{6} Pa
- 2.2 × 10
^{7} Pa
- 2.2 × 10
^{8} Pa
- 2.2 × 10
^{9} Pa

Water is flowing continuously from a tap having an internal diameter 8×10^{-3} m. The water velocity as it leaves the tap is 0.4 ms^{-1}. The diameter of the water stream at a distance 2×10^{-1} m below the tap is close to

- 7.5 × 10
^{-3} m
- 9.6 × 10
^{-3} m
- 3.6 × 10
^{-3} m
- 5.0 × 10
^{-3} m

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

- first increase then decrease
- increase
- decrease
- remain unchanged

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10^{3} kg/m^{3} and 2.2 × 10^{11} N/m^{2} respectively?

- 178.2 Hz
- 188.5 Hz
- 200.5 Hz
- 770 Hz

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

- 4
- 6
- 8
- 12

A child swinging on a swing in sitting position, stands up, then the time period of the swing will

- Remains same
- Decreases
- Increases
- Increase if the child is tall, decrease if the child is short

A wave y = a sin(ωt − kx) on a string meets with another wave producing a node at x = 0. Then the equation of the unknown wave is

- y = −a sin(ωt + kx)
- y = a sin(ωt + kx)
- y = a sin(ωt − kx)
- y = −a sin(ωt − kx)

If a spring has time period T, and is cut into n equal parts, then the time period of each part will be

- T
- T√n
- nT
- T/√n

A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

- L/4
- 4L
- L/2
- 2L

Moment of inertia of a circular wire of mass M and radius R about its diameter is

- (MR
^{2})/2
- MR
^{2}
- (MR
^{2})/4
- 2MR
^{2}

A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of

- ωl/(6g)
- ω
^{2}l^{2}/(2g)
- ω
^{2}l^{2}/(6g)
- ω
^{2}l^{2}/(3g)

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to

- t
^{1/2}
- t
^{1/4}
- t
^{3/2}
- t
^{3/4}

If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?

- 1 cm
- 2 cm
- 3 cm
- 4 cm

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx^{2} where a and b are constants. The work done in stretching the unstretched rubber band by L is

- aL
^{2}/2 + bL^{3}/3
- (aL
^{2} + bL^{3})/3
- aL
^{2} + bL^{3}
- (aL
^{2}/2 + bL^{3}/3)/2

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

- (√2)R
- R/2
- R/√2
- 2R

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

- zero
- -4Gm/r
- -6Gm/r
- -9Gm/r

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

- move tangentially to the originally orbit in the same velocity
- continue to move in its orbit with same velocity
- become stationary in its orbit
- move towards the earth

The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be

- 11/√2 m/s
- 11√2 km/s
- 22 km/s
- 11 km/s

The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is

- mgR
- 2mgR
- mgR/4
- mgR/2

A radar has a power of 1 Kw and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth = 6.4 x 10^{6} m) is

- 80 km
- 64 km
- 40 km
- 16 km

The escape velocity of a body depends upon mass as

- m
^{0}
- m
^{1}
- m
^{2}
- m
^{3}

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are 10 m/s^{2} and 6400 km respectively. The required energy for this work will be

- 6.4 X 10
^{8} Joules
- 6.4 X 10
^{9} Joules
- 6.4 X 10
^{10} Joules
- 6.4 X 10
^{11} Joules

When forces F_{1}, F_{2}, F_{3} are acting on a particle of mass m such that F_{2} and F_{3} are mutually perpendicular, then the particle remains stationary. If the force F_{1} is now removed then the acceleration of the particle is

- F
_{1}/m
- (F
_{2} - F_{3})/m
- (F
_{2}F_{3})/(mF_{1})
- F
_{2}/m

Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

- 10 N, 8 N
- 12 N, 6 N
- 13 N, 5 N
- 16 N, 2 N

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s^{2}, the reading of the spring balance will be

- 15 N
- 24 N
- 49 N
- 74 N

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

- g
- 5g/6
- g/2
- 2g/3

An object moving with a speed of 6.25 m/s, is decelerated at a rate given by dν/dt = 2.5√ν, where ν is the instantaneous speed. The time taken by the object, to come to rest, would be

- 8 s
- 4 s
- 2 s
- 1 s

A particle is moving with velocity v = K(yi + xj), where K is a constant. The general equation for its path is

- xy = constant
- y
^{2} = x + constant
- y
^{2} = x^{2} + constant
- y = x
^{2} + constant

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

- πv
^{4}/2g^{2}
- πv
^{2}/g^{2}
- πv
^{4}/g^{2}
- πv
^{2}/g

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

- 10 m
- 20√2 m
- 20 m
- 10√2 m

A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively

- g, g
- a, g
- g-a, g-a
- g-a, g

From a building two balls A and B are thrown such that A is thrown upwards A and B downwards (both vertically). If v_{A} and v_{B} are their respective velocities on reaching the ground, then

- their velocities depend on their masses
- V
_{B} > V_{A}
- V
_{A} = V_{B}
- V
_{A} > V_{B}

Which one of the following represents the correct dimensions of the coefficient of viscosity?

- ML
^{-2}T^{-2}
- MLT
^{-1}
- ML
^{-1}T^{-1}
- ML
^{-1}T^{-2}

Dimensions of 1/μ_{o}ε_{o}, where symbols have their usual meaning, are

- [L
^{2}T^{–2}]
- [LT
^{–1}]
- [L
^{–2}T^{2}]
- [L
^{–1}T]

Which of the following units denotes the dimensions ML^{2}/Q^{2}, where Q denotes the electric charge?

- weber (Wb)
- H/m
^{2}
- Wb/m
^{2}
- henry (H)

The physical quantities not having same dimensions are

- torque and work
- stress and Young's modulus
- speed and (μ
_{0}ε_{0})^{–1/2}
- momentum and Planck's constant

Identify the pair whose dimensions are equal

- force and work
- torque and work
- stress and energy
- force and stress

The dimension of magnetic field in M, L, T and C (coulomb) is given as

- MT
^{–1}C^{–1}
- MLT
^{–1}C^{–1}
- MT
^{2}C^{–2}
- MT
^{–2}C^{–1}

A particle has an initial velocity of 3i + 4j and an acceleration of 0.4i + 0.3j. Its speed after 10s is

- 7(√2) units
- 10 units
- 7 units
- 8.5 units

A light string passing over a smooth light pulley connects two blocks of masses m_{1} and m_{2} (vertically). If the acceleration of the system is g/8, then the ratio of the masses is

- 5:3
- 4:3
- 8:1
- 9:7

A block of mass m is placed on a surface with a vertical cross section given by y = x^{3}/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

- 1/6 m
- 1/3 m
- 1/2 m
- 2/3 m

A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is:

- ma
- 2 ma
- 3/2 ma
- 5/3 ma

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals μ. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR.

The values of the coefficient of friction μ and the distance x(=QR), are, respectively close to:

- 0.2 and 3.5 m
- 0.29 and 3.5 m
- 0.29 and 6.5 m
- 0.2 and 6.5 m

A spring of force constant 800 N/m has an extension of 5 cm. The work done is extending it from 5 cm to 15 cm is

- 32 J
- 8 J
- 24 J
- 16 J

A ball whose kinetic energy is E, is projected at an angle of 45° to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

- 0
- E
- E/2
- E/√2

A block of mass m=0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance (x/2) from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3 ms^{-1}. The total initial energy of the spring is:

- 1.5 J
- 0.6 J
- 0.3 J
- 0.8 J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8×10^{7} J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms^{-2}

- 6.45 × 10
^{-3} kg
- 9.89 × 10
^{-3} kg
- 12.89 × 10
^{-3} kg
- 2.45 × 10
^{-3} kg

Capacitance (in F) of a spherical conductor with radius 1 m is

- 10
^{-3}
- 1.1 X 10
^{-10}
- 9 X 10
^{-9}
- 10
^{-6}

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 × 10^{4} V/m, the charge density of the positive plate will be close to

- 6 × 10
^{–7} C/m^{2}
- 6 × 10
^{4} C/m^{2}
- 3 × 10
^{4} C/m^{2}
- 3 × 10
^{–7} C/m^{2}

A galvanometer having a coil resistance of 100 Ω gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A is:

- 2 Ω
- 0.1 Ω
- 3 Ω
- 0.01 Ω