IITJEE questions on Newton's laws motion and friction (Assignment 2)

Question 1
(i). A body of mass m moves along the positive x-axis, it starts at velocity v0 at t = o and
it is the origin initially. It is acted by the force such that
F = -kv
find the time in which it will come to rest
(a) t → ∞
(b) t = kt/m
(c) t = mt/k
(d) none of the above
(ii) Find the velocity of body as a function of time
(a) v0 exp (-kt/m)
(b) v0 exp (-mt/k)
(c) v0 exp (-t)
(d) none of the above
(iii). Find the value of x at which it velocity become 0
(a) mv0/k
(b) mv0/k2
(c) m/kv0
(d) none of the above
(iv) Find the velocity as a function of distance
(a) v0 + kx/m
(b) v0 - kx/m
(c) v0 - x/m
(d) none of the above
Question 2 : Matrix match type-
Column A
A boy of weight W is standing in an elevator. find the force of the boy feel
(a) when the elevator stand still
(b) when the elevator moving with constant velocity (v m/s) downward
(c) when the elevator moving with constant velocity (v m/s) upward
(d) moving up with acceleration (a m/s2 )
(e) moving down with acceleration (a m/s2 )
Column B
(P) F = W
(Q) F>W
(R) F< W
(S) no appropriate match
Question 3
(i). A 6 kg object is subject to three forces
F1= 20i + 30j N
F2 = 8i - 50j N
F3 = 2i + 2j N
find the acceleration of object
(a) 5i + 3j
(b) 5i - 3j
(c) 3i + 5j
(d) 3i - 5j
(ii). which of the following expression is correct if at t = 0, object is at origin and
velocity is v0  =i + j
(a) r = i(2.5 t2 +t) + j(t - 1.5 t2 )
(b) r = i(2.5  t2 - t) + j(t + 1.5 t2 )
(c) r = it - j t2
(d) none of the above

Question 4
A particle of weight W resting a smooth(frictional less) inclined plain AB with the help of  force F acting on the particle at angle θ with the line AB
find the force F and normal reaction
(a) (Wcosθ)/sinα, [Wcos(α - θ)]/cosθ
(b) (Wsinα)/cosθ, [Wcos(α + θ)]/cosθ
(c) (Wsinα)/cosθ, [Wsin(α + θ)]/cosθ
(d) none of the above
Question 5 : Match the column
S1 = frame of reference at rest
S2 = frame of reference at constant velocity
S3 = frame of reference at constant acceleration
S4 = frame of reference at uniform circular motion
A block A is at rest as seen from frame of reference S1
Column A
(a) S1
(b) S2
(c) S3
(d) S4
Column B
(P) ΣF ≠ 0
(Q) ΣF =0
(R) a = 0
(S) a ≠ 0
where ΣF is the resultant force and a is the acceleration of the body
Question 6
A boy pushes a mass with a force F. Confident of friction between body and floor is µm and between boy shoe and floor is µB There mass are M(block) and m(boy) respectively.
(i). What maximum force boy can apply without slipping
(a) µmmg
(b) µmMg
(c) µbg
(d) none of the above
(ii). What is the condition required to move the block without slipping
(a) µBm > M/m
(b) µBm > m/M
(c) µBm < M/m
(d) µBm < m/M
Question 1
(i) (a)
(ii) (a)
(iii) (a)
(iv) (b)
Question 2
(a) = (P)
(b) = (P)
(c) = (P)
(d) = (Q)
(e) = (R)
Question 3
(i) (b)
(ii) (a)
Question 4 (b)
Question 5
(a) → (Q), (R)
(b) → (Q), (R)
(c) → (Q), (S)
(d) → (Q), (S)
Question 6
(i) (c)
(ii) (a)

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