Q#8
Three rigid rods are joined to form an equilateral triangle ABC of side 1 m. Three particle carrying charges 20 µC each are attached to the vertices of the triangle. The whole system is at rest in an inertial frame. The resultant force on the charged particle at A has the magnitude(a) zero (b) 3.6 N (c) 3.6/3 N (d) 7.2 N
Answer: (a)
Since the charged particles are attached to rigid triangle ABC which is in rest in an inertial frame, so the particle at A is also at rest. It means the magnitude of resultant of forces acting on it is zero.
Q#9
A force F1acts on a particle so as to accelerate it from rest to a velocity v. The force F1 is then replaced by F2 which decelerates it to rest.
(a) F1 must be equal to F2 (b) F1 may be equal to F2
(c) F1 must be unequal to F2 (d) None of these
Answer: (b)
Neither the time nor the distance for accelerating and decelerating journey is mentioned. So both forces may or may not be equal.
Q#10
Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than the mass of B. Suppose the air exerts a constant and equal force of resistance on the two bodies.
(a) The two bodies will reach the same height
(b) A will go higher than B
(c) B will go higher than A (d) Any of the above three may happen depending on the speed with which the objects are thrown.
Answer: (b)
The force of resistance of air will add to retardation of both the body but its magnitude will depend upon mass of the objects as per "Newton's Second Law of Motion" and it will be equal to Force/mass. Since the force is equal on both the objects, the object having greater mass (A) will be retarded less, so it will go higher than B.
Q#11
A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes a time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will
(a) take a time longer than T to slide down the wedge
(b) take a time shorter than T to slide down the wedge
(c) remain at the top of the wedge
(d) jump off the wedge.
Answer: (c)
Both the wedge and block will be in free fall motion and have equal velocities downwards at any instant of time so there will be no relative motion.
Q#12
In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle's motion. A particle of mass m projected upward takes a time t1 in reaching the maximum height and t2 in the return journey to the original point. Then
(a) t1 < t2 (b) t1 > t2 (c) t1 = t2 (d) The relation between t1 and t2 depends on the mass of the particle.
Answer: (b)
Since F is in the direction of particle's motion it will add an acceleration in the direction of motion. Let it be a. Now magnitude of upward acceleration =a-g and downward acceleration = a + g. Clearly a + g > a – g and the particle travels same distance/height. So, the upward journey will take a longer time.
Q#13
A person standing on the floor of an elevator drops a coin. The coin reaches the floor of the elevator in a time t1 if the elevator is stationary and in time t2 if it is moving uniformly. Then
(a) t1 = t2 (b) t1 < t2 (c) t1 > t2 (d) t1 < t2 or t1 > t2 depending on whether the lift is going up or down.
Answer: (a)
The stationary and uniformly moving elevator are both inertial frame so value of acceleration due to gravity will remain the same in both conditions. The distance traveled by the coin with respect to the frame of elevator is equal in both cases. So the time taken will also be equal.
Q#14
A free 238U nucleus kept in a train emits an α - particle. When the train is stationary, a nucleus decays and a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x at time t after the decay. If the decay takes place while the train is moving at a uniform velocity v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay as measured by the passenger is
(a) x + vt (b) x – vt (c) x (d) depends on the direction of the train.
Answer: (c)
In both of the cases the frame of reference is inertial so with reference to the frame of train the separation too will be equal.
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