Laws of Motion & Friction · JEE Main previous year questions

Two identical strings X and Z made of same material have tension ${\mathrm{T}}_{\mathrm{X}}$ and ${\mathrm{T}}_{\mathrm{Z}}$ in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio ${\mathrm{T}}_{\mathrm{X}}/{\mathrm{T}}_{\mathrm{Z}}$ is

1. A.2.25
2. B.0.44
3. C.1.25
4. D.1.5

1. A.$2\sqrt{2gC}$
2. B.$2\sqrt{gC}$
3. C.$\sqrt{\frac{2gC}{ab}}$
4. D.$\sqrt{\frac{2g}{C}}$

1. A.0.5 mg
2. B.2 mg
3. C.0.75 mg
4. D.1 mg

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, $g=10{\text{ ms}}^{-2}$)

1. A.$1.5{\text{ ms}}^{-1}$
2. B.$1.7{\text{ ms}}^{-1}$
3. C.$2.0{\text{ ms}}^{-1}$
4. D.$1.9{\text{ ms}}^{-1}$

1. A.$r\sqrt{\frac{3}{2gh}}$
2. B.$r\sqrt{\frac{3}{4gh}}$
3. C.$\frac{1}{r}\sqrt{\frac{4gh}{3}}$
4. D.$\frac{1}{r}\sqrt{\frac{2gh}{3}}$

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70{\text{ ms}}^{-1}$ with respect to the man. The speed of the man with respect to the surface is :

1. A.$0.28{\text{ ms}}^{-1}$
2. B.$0.47{\text{ ms}}^{-1}$
3. C.$0.20{\text{ ms}}^{-1}$
4. D.$0.14{\text{ ms}}^{-1}$

1. A.$3.2{\text{ ms}}^{-2}$
2. B.$0.8{\text{ ms}}^{-2}$
3. C.$0{\text{ ms}}^{-2}$
4. D.$0.4{\text{ ms}}^{-2}$

1. A.$x=\left(\frac{I_1}{I_1+I_2}\right)d$ and $x=\left(\frac{I_2}{I_1-I_2}\right)d$
2. B.$x=\left(\frac{I_2}{I_1+I_2}\right)d$ and $x=\left(\frac{I_2}{I_1-I_2}\right)d$
3. C.$x=\left(\frac{I_1}{I_1-I_2}\right)d$ and $x=\left(\frac{I_2}{I_1+I_2}\right)d$
4. D.$x=\pm \frac{I_{1}d}{I_1-I_2}$

1. A.8 N
2. B.16 N
3. C.40 N
4. D.12 N

Light is incident normally on a completely absorbing surface with an energy flux of $25\mathrm{W}\mathrm{c}{\mathrm{m}}^{-2}$. If the surface has an area of $25\mathrm{c}{\mathrm{m}}^2$, the momentum transferred to the surface in 40 min time duration will be :

1. A.$6.3\times 10^{-4}\mathrm{Ns}$
2. B.$5.0\times 10^{-3}\mathrm{Ns}$
3. C.$1.4\times 10^{-6}\mathrm{Ns}$
4. D.$3.5\times 10^{-6}\mathrm{Ns}$

A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its $(1/n{)}^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be :

1. A.$\frac{2MgL}{n^2}$
2. B.nMgL
3. C.$\frac{MgL}{2n^2}$
4. D.$\frac{MgL}{n^2}$

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :-

1. A.180m/s, 80 Hz
2. B.180m/s, 120 Hz
3. C.320m/s, 120 Hz
4. D.320m/s, 80 Hz

1. A.$\frac{\sqrt{3}}{4}$
2. B.$\frac{1}{2}$
3. C.$\frac{\sqrt{3}}{2}$
4. D.$\frac{2}{3}$

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is ${\ell }_1$, and that below the piston is ${\ell }_2$, such that ${\ell }_1>{\ell }_2$. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravity)

1. A.$\frac{nRT}{g}\left[\frac{{\ell }_1-{\ell }_2}{{\ell }_1{\ell }_2}\right]$
2. B.$\frac{RT}{g}\left[\frac{2{\ell }_1+{\ell }_2}{{\ell }_1{\ell }_2}\right]$
3. C.$\frac{nRT}{g}\left[\frac{1}{{\ell }_2}+\frac{1}{{\ell }_1}\right]$
4. D.$\frac{RT}{ng}\left[\frac{{\ell }_1-3{\ell }_2}{{\ell }_1{\ell }_2}\right]$

A particle of mass m is moving in a straight line with momentum p. Starting at time $t=0$, a force $F=kt$ acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is :

1. A.$2\sqrt{\frac{k}{p}}$
2. B.$2\sqrt{\frac{p}{k}}$
3. C.$\sqrt{\frac{2p}{k}}$
4. D.$\sqrt{\frac{2k}{p}}$

1. A.$32\text{ N}$
2. B.$18\text{ N}$
3. C.$23\text{ N}$
4. D.$25\text{ N}$

1. A.$\tan \theta =\frac{1}{2\sqrt{3}}$
2. B.$\tan \theta =\frac{1}{2}$
3. C.$\tan \theta =\frac{2}{\sqrt{3}}$
4. D.$\tan \theta =\frac{1}{3}$

1. A.$\frac{2F}{\sqrt{mk}}$
2. B.$\frac{F}{\pi \sqrt{mk}}$
3. C.$\frac{\pi F}{\sqrt{mk}}$
4. D.$\frac{F}{\sqrt{mk}}$

Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B s slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is 425 Hz, the original frequency of B is :

1. A.430 Hz
2. B.420 Hz
3. C.428 Hz
4. D.422 Hz

A given object takes n times more time to slide down a $45^{\circ }$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ }$ incline. The coefficient of kinetic friction between the object and the incline is :

1. A.$\frac{1}{2-n^2}$
2. B.$1-\frac{1}{n^2}$
3. C.$\sqrt{1-\frac{1}{n^2}}$
4. D.$\sqrt{\frac{1}{1-n^2}}$

1. A.$10.3\mathrm{kg}$
2. B.$18.3\mathrm{kg}$
3. C.$27.3\mathrm{kg}$
4. D.$43.3\mathrm{kg}$

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

1. A.away from the wire
2. B.towards the wire
3. C.parallel to the wire along the current
4. D.parallel to the wire opposite to the current

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :

1. A.$\frac{1}{4}\mathrm{Hz}$
2. B.$\frac{1}{2\sqrt{2}}\mathrm{Hz}$
3. C.$\frac{1}{2}\mathrm{Hz}$
4. D.$2\mathrm{Hz}$