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NLM

513 Questions Start Advance Test
All Exams Allen Advance Errorless
Q176 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A car starts from rest to cover a distance $s$ . The coefficient of friction between the road and the tyres is $\mu$ . The minimum time in which the car can cover the distance $s$ is proportional to
A.
$\frac{1}{\mu}$
B.
$\frac{1}{\sqrt{\mu}}$
C.
$\mu$
D.
$\sqrt{\mu}$
Q177 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In the shown arrangement if $f_{1}$ , $f_{2}$ and T be the frictional forces on 2 kg block, 3 kg block and tension in the string respectively, then their values are
A.
2 N, 6 N, 3.2 N
B.
2N, 6N, 0N
C.
1N, 6N, 2N
D.
Data insufficient to calculate the required values
Q178 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In the figure given below, if all surface are assumed to be smooth and the force $F = 100 \mathrm{~N}$ . If acceleration of block $B$ of mass $20 \mathrm{~kg}$ is $a$ and tension in string connecting block $A$ of mass $20 \mathrm{~kg}$ is $T$ then just after when the force $F$ is applied
A.
T = 0 and $a = 5 \, ms^{-2}$
B.
$T = 100\mathrm{N}$ and $a = 0$
C.
$T = 200\mathrm{N}$ and $a = 5\mathrm{ms}^{-2}$
D.
None of these
Q179 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The block of mass m is placed on a rough horizontal floor and it is pulled by an ideal string as shown by a constant force F. As the block moves towards right the friction force on block
A.
remains constant
B.
increases
C.
decreases
D.
can be said
Q180 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Two blocks each of mass 20 kg are connected by an ideal string and this system is kept on rough horizontal surface as shown. Initially the string is just tight then a horizontal force F = 120 N is applied on one block as shown. If friction coefficient at every contact is $\mu = 0.5$ then which of the following represents the correct free body diagram.
A.
B.
C.
D.
All of the above
Q181 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle is moving along a circular path with a constant speed. The acceleration of the particle is constant in
A.
magnitude
B.
direction
C.
both magnitude and direction
D.
neither magnitude nor direction
Q182 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle moves in $x - y$ plane. The position vector of particle at any time $t$ is $\vec{r} = \left[(2t)\hat{i} + (2t^2)\hat{j}\right]\mathrm{m}$ . The rate of change of $\theta$ at time $t = 2\mathrm{s}$ . (where $\theta$ is the angle which its velocity vector makes with positive $x$ -axis) is
A.
$\frac{2}{17}$ rads $^{-1}$
B.
$\frac{1}{14}$ rads $^{-1}$
C.
$\frac{4}{7}$ rads $^{-1}$
D.
$\frac{6}{5}$ rads $^{-1}$
Q183 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Two identical ideal springs of spring constant $1000 \, Nm^{-1}$ are connected by a pulley as shown in figure and this arrangement is established in the vertical plane. The pulley is ideal and string passing over pulley is massless. At equilibrium of pulley $\theta$ is $60^{\circ}$ and the masses $m_{1}$ and $m_{2}$ are 2 kg and 3 kg, respectively. Then the elongation in each spring when $\theta = 60^{\circ}$ is
A.
$1.6\sqrt{3}\mathrm{cm}$
B.
$1.6\mathrm{cm}$
C.
$4.8\mathrm{cm}$
D.
None of these
Q184 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A sphere of mass m is held between two smooth inclined walls A and B. For $\sin(37^{\circ})=\frac{3}{5}$ , the normal reaction of the wall (2) is equal to
A.
mg
B.
$mg \sin(74^{\circ})$
C.
$mg \cos(74^{\circ})$
D.
None of these
Q185 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block A of mass 2 kg rests on another block B of mass 8 kg which rests on a horizontal floor. The coefficient of friction between A and B is 0.2 while between B and floor is 0.5. When a horizontal force $25\mathrm{N}$ is applied on $B$ , the frictional force acting between $A$ and $B$ is
A.
$0\mathrm{N}$
B.
$3.9\mathrm{N}$
C.
$5\mathrm{N}$
D.
$49\mathrm{N}$
Q186 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block starts moving up a fixed inclined plane of inclination $60^{\circ}$ with a velocity of $20\mathrm{ms}^{-1}$ and stops after 2 s. The approximate value of coefficient of friction is $(g = 10\mathrm{ms}^{-2})$
A.
3
B.
3.3
C.
0.27
D.
0.33
Q187 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A point on the periphery of rotating disc has its acceleration vector making on angle $30^{\circ}$ with velocity vector then the ratio of magnitude of centripetal acceleration to tangential acceleration is
A.
$\sin (30^{\circ})$
B.
$\cos (30^{\circ})$
C.
$\tan (30^{\circ})$
D.
None of these
Q188 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Find the only correct statement from the following statements
A.
A body has a constant velocity and still it can have a varying speed
B.
A body has a constant speed but it can have a varying velocity
C.
A body having constant speed cannot have any acceleration
D.
A body in motion under a force acting upon it must always have work done upon it
Q189 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A smooth sphere of radius $R$ and mass $M$ is placed on the smooth horizontal floor. Another smooth particle of mass $m$ is placed on the sphere and a horizontal force $F$ is applied on the sphere as shown. If the particle does not slip on the sphere then the value of force $F$ is
A.
$F = mg\cot \theta$
B.
$F = Mg\cot \theta$
C.
$F = (m + M)g \cot \theta$
D.
$F = (m + M)g\tan \theta$
Q190 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The contact force exerted by a body on another body is perpendicular to the surfaces in contact. Then,
A.
the surfaces in contact must be frictionless
B.
the force of friction between the bodies may not be zero
C.
the contact force equals the normal reaction
D.
the contact force equals the friction
Q191 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A rod AB of mass 10 kg tied with a string at C such that AC = BC and rod remains in equilibrium then friction force by horizontal surface will be
A.
50 N towards right
B.
50 N towards left
C.
100 N
D.
None of these
Q192 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block of mass m is moving on a rough horizontal surface where coefficient of friction between block and surface is $\mu=0.5$ . At t=0, block is moving with a velocity $\vec{v}$ . Then a horizontal force F=2t is applied on it in the direction of velocity, where t represents time, then the speed of block after the application of force
A.
decreases
B.
increases
C.
first decreases then increases
D.
first increases then decreases
Q193 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A circular disc of radius r = 5 m is rotating in horizontal plane about y-axis. y-axis a vertical axis passing through the centre of disc and x-z is the horizontal plane at ground. The height of disc above ground is h = 5 m. Small particles are ejecting from disc in horizontal direction with speed $12 \, ms^{-1}$ from the circumference of disc then the distance of these particles from origin when they hits x-z plane is
A.
5 m
B.
12 m
C.
13 m
D.
None of these
Q194 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20 m. The length of each propeller blade is 12 m. A tip of the propeller breaks off when the propeller is vertical. At that instant, the period of the motion of the propeller is 1.2 second. The fragment files off horizontally, falls and strikes the ground at point P. In figure, the distance from the base of the pylon to the point where the fragment strikes the ground is closest to
A.
120 m
B.
130 m
C.
140 m
D.
160 m
Q195 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Two blocks A and B of masses m and 2m, respectively are held at rest such that the string is in natural length. Find out the accelerations of both the blocks just after release.
A.
$g \downarrow, g \downarrow$
B.
$\frac{g}{3} \downarrow, \frac{g}{3} \uparrow$
C.
0, 0
D.
$g \downarrow, 0$
Q196 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In the arrangement shown, the wedge of mass $M$ moves towards left with an acceleration $a$ . All surfaces are smooth. The acceleration of mass $m$ relative to wedge is
A.
$\frac{a}{2}$
B.
$\frac{2Ma}{m}$
C.
$\frac{2(M + m)a}{m}$
D.
$\frac{(M + m)a}{m}$
Q197 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body $A$ rests on $B$ and friction coefficient between $A$ and $B$ is $\mu$ . Block $M$ is placed on a frictionless surface. Then (i) (ii)
A.
the maximum possible value of $F$ so that both bodies move together in case (i) is $\mu(m+M)g$
B.
the maximum possible value of F so that both bodies move together in case (i) is $\mu mg$
C.
the maximum possible value of $F$ so that both bodies move together in case (ii) is $\mu(M+m)g$
D.
the maximum possible value of $F$ so that both bodies move together in case (ii) is $\mu Mg$
Q198 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A bicycle is in motion. When it is not pedalled, the force of friction exerted by the ground on two wheels is such that it acts
A.
in the backward direction on the front wheel and in the forward direction on the rear wheel
B.
in the forward direction on the front wheel and in the backward direction on rear wheel
C.
in the backward direction on both the front and the rear wheels
D.
in the forward direction on both the front and the rear wheels
Q199 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle is moving in a circular path and its acceleration vector is making an angle of $30^{\circ}$ with the velocity vector, then the ratio of centripetal acceleration to its tangential acceleration is
A.
$\frac{1}{2}$
B.
$\frac{\sqrt{3}}{2}$
C.
$\frac{1}{\sqrt{3}}$
D.
$\sqrt{3}$
Q200 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is moving is x-y plane as shown in a circular path of radius 2 m. At a certain instant when the body is crossing the positive y-axis its acceleration is $(6\hat{i}-8\hat{j})\mathrm{ms}^{-2}$ . Then its angular acceleration and angular velocity at this instant will be
A.
$-3\hat{k}$ rads $^{-2}$ and $-2\hat{k}$ rads $^{-1}$ respectively
B.
$+3\hat{k}$ rads $^{-2}$ and $+2\hat{k}$ rads $^{-1}$ respectively
C.
$-4\hat{k}$ rads $^{-2}$ and $-\sqrt{3}\hat{k}$ rads $^{-1}$ respectively
D.
$+4\hat{k}$ rads $^{-2}$ and $+\sqrt{3}\hat{k}$ rads $^{-1}$ respectively