JEE Main Practice — Physics Set 7

Unpolarised light of intensity 64 W/m$^2$ passes through two ideal polarisers whose transmission axes are at $60^\circ$ to each other. The intensity of the emergent light (in W/m$^2$) is ______.

Correct answer: 8

A Young's double-slit apparatus with slit separation 0.6 mm and screen distance 1 m is illuminated simultaneously by wavelengths 450 nm and 600 nm. The minimum distance from the central maximum (in mm) at which bright fringes of the two wavelengths coincide is ______.

Correct answer: 3

A transverse wave on a string is described by $y=0.05\sin\left[2\pi(10t-0.5x)\right]$ with $x$, $y$ in metre and $t$ in second. The speed of the wave is

1. A.5 m/s
2. B.20 m/s✓
3. C.0.05 m/s
4. D.10 m/s

Correct answer: B

The speed of sound in air at $27^\circ$C is 340 m/s. Its speed at $127^\circ$C is approximately

1. A.453 m/s
2. B.340 m/s
3. C.393 m/s✓
4. D.294 m/s

Correct answer: C

A string 1 m long, fixed at both ends, has linear mass density 0.01 kg/m and tension 100 N. The frequency of its third harmonic is

1. A.150 Hz✓
2. B.50 Hz
3. C.100 Hz
4. D.300 Hz

Correct answer: A

The fundamental frequency of an open organ pipe is 300 Hz. A pipe of the same length closed at one end will have its first overtone at

1. A.600 Hz
2. B.150 Hz
3. C.300 Hz
4. D.450 Hz✓

Correct answer: D

A tuning fork A of frequency 256 Hz produces 4 beats per second with fork B. When B is loaded with a little wax, the beat frequency becomes 2 per second. The original frequency of B was

1. A.252 Hz
2. B.258 Hz
3. C.260 Hz✓
4. D.254 Hz

Correct answer: C

A car moves at 34 m/s towards a large vertical wall, sounding a horn of frequency 500 Hz. The speed of sound is 340 m/s. The frequency of the echo heard by the driver is approximately

1. A.611 Hz✓
2. B.556 Hz
3. C.550 Hz
4. D.409 Hz

Correct answer: A

A string 60 cm long, fixed at both ends, vibrates in three loops at a frequency of 150 Hz. The speed of transverse waves on the string (in m/s) is ______.

Correct answer: 60

In a resonance-tube experiment with a tuning fork of 500 Hz, the first and second resonances occur at air-column lengths of 16 cm and 50 cm. The speed of sound in air (in m/s) is ______.

Correct answer: 340

A force $F=3x^2$ N acts on a particle along the $x$-axis. The work done by the force as the particle moves from $x=0$ to $x=2$ m is

1. A.12 J
2. B.6 J
3. C.4 J
4. D.8 J✓

Correct answer: D

A pump lifts 600 kg of water per minute to a height of 20 m. The minimum power of the pump is ($g=10$ m/s$^2$)

1. A.2 kW✓
2. B.120 kW
3. C.1 kW
4. D.20 kW

Correct answer: A

A 2 kg block moving at 4 m/s on a smooth horizontal surface hits a light spring of force constant 800 N/m fixed at its other end. The maximum compression of the spring is

1. A.0.1 m
2. B.0.4 m
3. C.0.2 m✓
4. D.0.02 m

Correct answer: C

A 0.5 kg stone tied to a string of length 0.4 m is whirled in a vertical circle with just enough speed at the lowest point to complete the circle. The tension in the string at the lowest point is ($g=10$ m/s$^2$)

1. A.5 N
2. B.30 N✓
3. C.25 N
4. D.15 N

Correct answer: B

A 2 kg ball moving at 6 m/s collides head-on elastically with a stationary 4 kg ball. The fraction of the initial kinetic energy transferred to the 4 kg ball is

1. A.$\frac89$✓
2. B.$\frac49$
3. C.$\frac13$
4. D.$\frac23$

Correct answer: A

A bullet of mass 20 g moving horizontally at 300 m/s embeds itself in a 1.98 kg block attached to a horizontal spring of force constant 900 N/m on a smooth floor. The maximum compression of the spring is approximately

1. A.10 cm
2. B.14.1 cm✓
3. C.20 cm
4. D.7.1 cm

Correct answer: B

A 2 kg particle moves along the $x$-axis in a potential $U(x)=x^2-4x+6$ (J, with $x$ in metre). If its total mechanical energy is 11 J, its maximum speed (in m/s) is ______.

Correct answer: 3

A 5 kg block starts from rest and is pushed 10 m along a rough horizontal floor ($\mu_k=0.2$) by a constant horizontal force of 30 N. Its kinetic energy (in joule) at the end of the 10 m is ______. ($g=10$ m/s$^2$)

Correct answer: 200