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

Center of Mass question

2022 · 27 Jun · Shift 1 · Q46
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. /Center of Mass
  5. /2022 · 27 Jun · Shift 1 · Q46

Center of Mass question

2022 · 27 Jun · Shift 1 · Q46

JEE MainPhysicsCenter of MassMCQ+4 / −1
Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is :
  1. A
    4 cm towards the 10 kg block
  2. B
    2 cm away from the 10 kg block
  3. C
    2 cm towards the 10 kg block
  4. D
    4 cm away from the 10 kg block
View written solutionFree

Correct answer: C

  1. Let the 10 kg block move by +6 cm+6\,\text{cm}+6cm along the line toward the 30 kg block.

  2. To keep the centre of mass unchanged, the net change in ∑mixi\sum m_i x_i∑mi​xi​ must be zero: m1 Δx1+m2 Δx2=0m_1\,\Delta x_1 + m_2\,\Delta x_2 = 0m1​Δx1​+m2​Δx2​=0 where m1=10 kg,Δx1=+6 cm,m2=30 kg.m_1=10\,\text{kg},\quad \Delta x_1=+6\,\text{cm},\quad m_2=30\,\text{kg}.m1​=10kg,Δx1​=+6cm,m2​=30kg.

  3. Substitute: 10(6)+30 Δx2=010(6) + 30\,\Delta x_2 = 010(6)+30Δx2​=0 60+30 Δx2=060 + 30\,\Delta x_2 = 060+30Δx2​=0 Δx2=−2 cm\Delta x_2 = -2\,\text{cm}Δx2​=−2cm

  4. The negative sign means the 30 kg block must move in the opposite direction, i.e. towards the 10 kg block by 2 cm2\,\text{cm}2cm.

  5. Check with options:

  • A: 444 cm towards the 10 kg block →\rightarrow→ incorrect
  • B: 222 cm away from the 10 kg block →\rightarrow→ incorrect
  • C: 222 cm towards the 10 kg block →\rightarrow→ correct
  • D: 444 cm away from the 10 kg block →\rightarrow→ incorrect

Therefore, the correct answer is Option C.

PreviousNext

More from Center of Mass

  • What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)2022 · MCQ
  • In two different experiments, an object of mass 5 kg moving with a speed of 25 ms−1 hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of…2022 · MCQ
  • The distance of centre of mass from end A of a one dimensional rod (AB) having mass density ρ=ρ0​(1−L2x2​)kg/m and length L (in meter) is α3L​m. The value…2022 · Numerical
  • A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms − 1. The velocity of the running man was ​ ms − 1,…2022 · Numerical
  • Two bodies of mass 1 kg and 3 kg have position vectors i^+2j^​+k^ and −3i^−2j^​+k^ respectively. The magnitude of position vector of centre of mass of this system will be similar…2022 · MCQ
  • If momentum of a body is increased by 20%, then its kinetic energy increases by2022 · MCQ
  • A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms − 1 and 40 ms − 1 respectively. The velocity of the third piece will…2022 · MCQ
  • Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :2022 · MCQ