Option 1 : The body with more mass will have more momentum 
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CONCEPT:
P = mv where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.
The kinetic energy in terms of momentum is given by: \(K=\frac{P^2}{2m}\) where K is the kinetic energy of the body, P is the momentum of the body and m is the mass of the body. EXPLANATION: Given that the Kinetic energy of both masses is the same. K1 = K2 \(\frac{P_1^2}{2M_1}=\frac{P_2^2}{2M_2}\) \(\frac{P_1^2}{P_2^2}=\frac{2M_1}{2M_2}\) \(\frac{P_1^2}{P_2^2}=\frac{M_1}{M_2}\) P2 ∝ M P ∝ √M So the more mass will give the more momentum. Hence the correct answer is option 1 i.e. The body with more mass will have more momentum India’s #1 Learning Platform Start Complete Exam Preparation
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Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track (Fig. 6.16). Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given θ1 = 30°, θ2 = 60°, and h = 10 m, what are the speeds and times taken by the two stones?
The given question can be illustrated using the figure below: AB and AC are two smooth planes inclined to the horizontal at ∠θ1 and ∠θ2 respectively. The height of both the planes is the same, therefore, both the stones will reach the bottom with same speed. As P.E. at O = K.E. at A = K.E. at B Therefore, mgh = 1/2 mv12 = 1/2 mv22 ∴ v1 = v2 As it is clear from fig. above, acceleration of the two blocks are As θ2 > θ1 ∴ a2 > a1 From v = u + atat As t ∝ 1/a, and a2 > a1 ∴ t2 < t1 That is, the second stone will take lesser time and reach the bottom earlier than the first stone.
The temperature of a body is its average in the various (spin, magnetization, kinetic...) energy degrees of freedom, not a simple kinetic energy value. We measure temperature by applying a thermometer, and waiting for the thermometer to come to the same temperature as the sample, which happens because of the so-called zeroth law of thermodynamics: heat travels from the hotter of two bodies in contact, to the cooler. When heat stops making a net increase or decrease in the temperature of the thermometer, that tells us the temperature of the sample is the same as the temperature of the thermometer, and thus the temperature of the sample-and-thermometer-probe is what the thermometer display indicates. We can do this because the probe thermal contact does NOT achieve a temperature difference with the sample, but converges to the same temperature. The effect of individual interactions is not unimportant; it gives rise to internal fluctuations in any given speck of the system, some of which are observable (Brownian motion is an example; the rushing sound heard in a conch shell is another). The microscopic picture of elements of a gas, for instance, can have a wide range of gas molecule velocities. Single molecules thus do NOT have a measurable statistical property of temperature unless we make a long-time observation and average the various wanderings over many seconds, or apply an ergodic principle (a very useful conceit, ergodicity: the time average is equal to the population-of- other-molecules average). Ergodic principles are mathematically poorly founded (the theorems are weak ones) but physicists use them (and sometimes call them theorems, if no mathematicians are present). The temperature of a gas particle is inferred routinely from the average that communicates from many particles slowly to a massive thermometer bulb... Open in App
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Two bodies have linear momentum, the kinetic energy will be more for
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