## Lakshya Education MCQs

Question: F=3^i+6^j8^k

s=2^i+5^j+2^k

If W =F.s find W.
Options:
 A. 8 N. m B. 20 N. m C. 5 N. m D. None of these
: A

F=3^i+6^j8^k s=2^i+5^j+2^k W =F.s = (3^i+6^j8^k).(2^i+5^j+2^k) = (-6) + (30) + (-16) (^i.^i=1&^i.^j=0) W = 8 N.m

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## More Questions on This Topic :

Question 1. Given F=(xy2)^i+(x2y)^jN. The work done by F when a particle is taken along the semicircular path OAB where the coordinates of B are (4,0) is

1.    653J
2.    752J
3.    734J
4.    Zero
: D

GivenF=(xy2)^i+(x2y)^j W = Fxdx+Fydy = xy2dx+x2ydy = 12d(x2y2)=[x2y22](4,0)(0,0)=0
Question 2. A 50 g bullet moving with velocity 10 m/s strikes a block of mass 950 g at rest and gets embedded in it. The loss in kinetic energy will be
1.    100%
2.    95%
3.    5%
4.    50%
: B Initial K.E. of system = K.E. of the bullet = 12msv2s By the law of conservation of linear momentum msvs+0=msys×vsys vsys=msvsmsys=50×1050+950=0.5m/s Fractional loss in K.E. = 12msv2s12msysv2sys12msv2s By substituting ms=50×103kg,vs=10m/s msys=1kg,vsys=0.5m/s we get Fractional loss = 95100 Percentage loss = 95 %
Question 3. A small block of mass 2 kg is kept on a rough inclined surface of inclination θ=30 fixed in a lift. The lift goes up with a uniform speed of 1 ms1 and the block does not slide relative to the inclined surface. The work done by the force of friction on the block in a time interval of 2 s is.
1.    Zero
2.    9.8 J
3.    29.4 J
4.    16.9 J
: B

Since the lift's speed is constant, in the absence of acceleration, there will be no pseudo-force (referring to the lift as the frame of reference) or additional reaction/thrust due to inclined plane (referring to ground as the reference frame) on the particle.
Therefore, friction =mg sinθacting along the plane.
Distance moved by the particle (or lift) in time t=vt Work done in time t=(mg sinθ)vt(cos(90-θ))=mgsin2θvt Substituting the Values we get Work = 9.8 J
Question 4. A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?

1.    The light body
2.    The heavy body
3.    Both have equal momentum
4.    It is not possible to say anything without additional information