Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Laws of Motion question

2024 · 9 Apr · Shift 1 · Q75
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Laws of Motion
  5. /2024 · 9 Apr · Shift 1 · Q75

Laws of Motion question

2024 · 9 Apr · Shift 1 · Q75

JEE MainPhysicsLaws of MotionMCQ+4 / −1
A light unstretchable string passing over a smooth light pulley connects two blocks of masses m1m_1m1​ and m2m_2m2​. If the acceleration of the system is g8\frac{g}{8}8g​, then the ratio of the masses m2m1\frac{m_2}{m_1}m1​m2​​ is :
  1. A
    5:35: 35:3
  2. B
    8:18: 18:1
  3. C
    9:79: 79:7
  4. D
    4:34: 34:3
View written solutionFree

Correct answer: C

  1. Model the system as an Atwood machine

For two masses m1m_1m1​ and m2m_2m2​ connected by a light string over a smooth light pulley, the acceleration is

a=(m2−m1)gm1+m2a = \frac{(m_2-m_1)g}{m_1+m_2}a=m1​+m2​(m2​−m1​)g​

assuming m2>m1m_2 > m_1m2​>m1​.

Given:

a=g8a = \frac{g}{8}a=8g​

So,

(m2−m1)gm1+m2=g8\frac{(m_2-m_1)g}{m_1+m_2} = \frac{g}{8}m1​+m2​(m2​−m1​)g​=8g​

Cancel ggg:

m2−m1m1+m2=18\frac{m_2-m_1}{m_1+m_2} = \frac{1}{8}m1​+m2​m2​−m1​​=81​

  1. Solve for the ratio

Cross-multiplying,

8(m2−m1)=m1+m28(m_2-m_1)=m_1+m_28(m2​−m1​)=m1​+m2​

8m2−8m1=m1+m28m_2-8m_1=m_1+m_28m2​−8m1​=m1​+m2​

8m2−m2=8m1+m18m_2-m_2=8m_1+m_18m2​−m2​=8m1​+m1​

7m2=9m17m_2=9m_17m2​=9m1​

Hence,

m2m1=97\frac{m_2}{m_1}=\frac{9}{7}m1​m2​​=79​

So the ratio is

m2:m1=9:7m_2:m_1 = 9:7m2​:m1​=9:7

  1. Check options
  • A: 5:35:35:3 ✗
  • B: 8:18:18:1 ✗
  • C: 9:79:79:7 ✓
  • D: 4:34:34:3 ✗

Therefore, the correct option is C.

PreviousNext

More from Laws of Motion

  • A 1 kg mass is suspended from the ceiling by a rope of length 4 m. A horizontal force 'F' is applied at the mid point of the rope so that the rope makes an angle of 45∘ with respect to the vertical axis… Includes diagram2024 · MCQ
  • Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of…2024 · MCQ
  • All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is : Includes diagram2024 · MCQ
  • A block of mass m is placed on a surface having vertical crossection given by y=x2/4. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:2024 · MCQ
  • Three blocks A,B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure The tensions T 1​ and T 2​ in the string are respectively : Includes diagram2024 · MCQ
  • In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane… Includes diagram2024 · MCQ
  • A block of mass 5 kg is placed on a rough inclined surface as shown in the figure. If F1​​ is the force required to just move the block up the inclined plane and F2​​ is the force required to… Includes diagram2024 · MCQ
  • A light string passing over a smooth light fixed pulley connects two blocks of masses m1​ and m2​. If the acceleration of the system is g/8, then the ratio of masses is: Includes diagram2024 · MCQ