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There are two bodies X and Y with equal kinetic energy but different masses m and 4m respectively. The ratio of their linear momentum is-
- a)1:2
- b)4:1
- c)1:√2
- d)1:4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
There are two bodies X and Y with equal kinetic energy but different m...
X and Y have equal kinetic energy but their masses are m and 4m respectively.
► 1/2 m1v12 = 1/2 m2v22
► mv12 = 4m * v22
► v1 : v2 = 2 : 1
Hence the ratio of their linear momentum is:
m1v1 : m2v2 = m * 2v : 4m * v = 1 : 2
► 1/2 m1v12 = 1/2 m2v22
► mv12 = 4m * v22
► v1 : v2 = 2 : 1
Hence the ratio of their linear momentum is:
m1v1 : m2v2 = m * 2v : 4m * v = 1 : 2
Most Upvoted Answer
There are two bodies X and Y with equal kinetic energy but different m...
Kinetic energy E=1/2 mv^2 now, from here we can derive linear momentum i.e. P=mv=√(2mE) so, P1/ P2 = √(m1/m2)= √ (m/4m)=√1/4=1/2
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Community Answer
There are two bodies X and Y with equal kinetic energy but different m...
We know that kinetic energy (KE) is given by:
KE = 1/2 mv^2
Since both bodies have the same kinetic energy, we can write:
1/2 mv_X^2 = 1/2 (4m)v_Y^2
Simplifying, we get:
v_Y = (1/2)v_X
Now, linear momentum (p) is given by:
p = mv
Using the above equation for velocity, we can write:
p_Y = 4m(1/2)v_X = 2mv_X
The ratio of their linear momentum can be written as:
p_X : p_Y = p_X : 2p_X = 1 : 2
Therefore, the answer is (a) 1 : 2.
KE = 1/2 mv^2
Since both bodies have the same kinetic energy, we can write:
1/2 mv_X^2 = 1/2 (4m)v_Y^2
Simplifying, we get:
v_Y = (1/2)v_X
Now, linear momentum (p) is given by:
p = mv
Using the above equation for velocity, we can write:
p_Y = 4m(1/2)v_X = 2mv_X
The ratio of their linear momentum can be written as:
p_X : p_Y = p_X : 2p_X = 1 : 2
Therefore, the answer is (a) 1 : 2.
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There are two bodies X and Y with equal kinetic energy but different masses m and 4m respectively. The ratio of their linear momentum is-a)1:2b)4:1c)1:√2d)1:4Correct answer is option 'A'. Can you explain this answer?
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