Laws of Motion

Question 477
CBSEENPH11020263

A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

  • 44%

  • 50%

  • 56%

  • 62%

Solution

C.

56%

Question 478
CBSEENPH11020270

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

  • 2g/3

  • g/2

  • 5g/6

  • g

Solution

B.

g/2

For the mass m,
mg-T = ma

As we know, a = Rα    ... (i)
So, mg-T = mRα
Torque about centre of pully
T x R = mR2α ...... (ii)
From Eqs. (i) and (ii), we get 
a = g/2
Hence, the acceleration of the mass of a body fall is g/2.

Question 479
CBSEENPH11020301

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of 1.5 x10–2N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

  • 0.0125 Nm-1

  • 0.1 Nm-1

  • 0.05 Nm-1

  • 0.025 Nm-1

Solution

D.

0.025 Nm-1


The force of surface tension acting on the slider balances the force due to the weight.

⇒F = 2Tl = w
⇒2T(0.3) = 1.5 x 10–2
⇒T = 2.5 x 10–2 N/m

Question 480
CBSEENPH11020304

A liquid in a beaker has temperature θ(t) at time t and θ0 is temperature of surroundings, then according to Newton's law of cooling the correct graph between loge (θ – θ0) and t is

Solution

A.

According to Newton's law of cooling.
dθ over dt space proportional to left parenthesis straight theta minus straight theta subscript straight o right parenthesis
rightwards double arrow fraction numerator begin display style dθ end style over denominator begin display style dt end style end fraction space equals space minus straight k left parenthesis straight theta minus straight theta subscript straight o right parenthesis
integral fraction numerator begin display style dθ end style over denominator begin display style straight theta minus straight theta subscript straight o end style end fraction space equals space integral negative kdt space
rightwards double arrow space In space left parenthesis straight theta minus straight theta subscript straight o right parenthesis space equals space minus kt plus straight c
Hence the plot of ln(θ – θ0) vs t should be a straight line with negative slope.

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