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

Work Power and Energy question

2013 · Shift 2 · Q44
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 Advanced
  3. /Physics
  4. /Work Power and Energy
  5. /2013 · Shift 2 · Q44

Work Power and Energy question

2013 · Shift 2 · Q44

JEE AdvancedPhysicsWork Power and EnergyMCQ+3 / −0.75
A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s2) JEE Advanced 2013 Paper 2 Offline Physics - Work Power & Energy Question 20 English ComprehensionThe magnitude of the normal reaction that acts on the block at the point Q is
  1. A
    7.5 N
  2. B
    8.6 N
  3. C
    11.5 N
  4. D
    22.5 N
View written solutionFree

Correct answer: A

  1. Energy conservation from top to point QQQ

    The block starts from rest, so initially Ki=0.K_i = 0.Ki​=0.

    Up to point QQQ, energy lost to friction is given as Wf=150 J.W_f = 150\text{ J}.Wf​=150 J.

    From the figure, the block moves from the top of the circular track to point QQQ such that the vertical drop is the radius: h=R=40 m.h = R = 40\text{ m}.h=R=40 m.

    Hence loss in gravitational potential energy is mgh=(1)(10)(40)=400 J.mgh = (1)(10)(40) = 400\text{ J}.mgh=(1)(10)(40)=400 J.

    Therefore kinetic energy at QQQ is KQ=400−150=250 J.K_Q = 400 - 150 = 250\text{ J}.KQ​=400−150=250 J.

    So, 12mv2=250\frac{1}{2}mv^2 = 25021​mv2=250 12(1)v2=250\frac{1}{2}(1)v^2 = 25021​(1)v2=250 v2=500.v^2 = 500.v2=500.

  2. Radial force balance at QQQ

    At point QQQ, the radius is horizontal, so the inward radial direction is horizontal.

    The weight mgmgmg acts vertically downward, hence it has no radial component at QQQ.

    Friction acts tangentially, so it also has no radial component.

    Therefore, the only force providing centripetal force is the normal reaction NNN: N=mv2R.N = \frac{mv^2}{R}.N=Rmv2​.

    Substituting the values, N=(1)(500)40=12.5 N.N = \frac{(1)(500)}{40} = 12.5\text{ N}.N=40(1)(500)​=12.5 N.

  3. Compare with options

    The computed value is N=12.5 N.N = 12.5\text{ N}.N=12.5 N.

    This does not match any option exactly. The closest option is 11.5 N11.5\text{ N}11.5 N, but that is not equal to the calculated result.

  4. Comparison with stored answer

    Stored correct answer is A: 7.5 N7.5\text{ N}7.5 N, which is inconsistent with the standard energy and centripetal-force analysis.

    If the figure instead implies a different vertical drop, the result may change, but with the usual interpretation of point QQQ as the side point of the circular arc, the correct value is 12.5 N12.5\text{ N}12.5 N.

    Since 12.5 N12.5\text{ N}12.5 N is not present in the options, the question/options likely contain an error.

PreviousNext

More from Work Power and Energy

  • A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the… Includes diagram2013 · MCQ
  • A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as… Includes diagram2011 · Numerical
  • A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes… Includes diagram2011 · Multiple correct
  • A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the… Includes diagram2010 · MCQ
  • A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s2, find the work done (in joules) by the string on the block of mass 0.36 kg during… Includes diagram2009 · Numerical
  • Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B…2009 · Numerical
  • A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have… Includes diagram2008 · MCQ
  • A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle θ at which the speed of the bob is half of that at A, satisfies, Includes diagram2008 · MCQ