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513 Questions Start Advance Test
All Exams Allen Advance Errorless
Q251 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to $n$ th mass is
A.
$\frac{mMg}{nm+M}$
B.
$\frac{mMg}{nmM}$
C.
mg
D.
mng
Q252 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A ball of mass 400 g is dropped from a height of 5 m. A boy on the ground hits the ball vertically upwards with a bat with an average force of 100 N so that it attains a vertical height of 20 m. The time for which the ball remains in contact with the bat is $\left(g=10\ \mathrm{ms}^{-2}\right)$
A.
0.12 sec
B.
0.08 sec
C.
0.04 sec
D.
12 sec
Q253 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A uniform chain of length $L$ has one of its ends attached to the wall at point $A$ , while $\frac{3L}{4}$ of the length of chain is lying on table as shown in figure. The minimum coefficient of friction between table and chain, so that chain remains in equilibrium is
A.
$\frac{1}{3}$
B.
$\frac{1}{4}$
C.
$\frac{3}{4}$
D.
$\frac{1}{5}$
Q254 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block is resting on a horizontal plate in the XY plane and co-efficient of friction between block and the plate is $\mu$ . The plate begins to move with velocity $v = bt^{2}$ in X-direction. At what time will the block starts sliding from plate
A.
$\frac{\mu b}{g}$
B.
$\frac{\mu bg}{2}$
C.
$\frac{\mu g}{b}$
D.
$\frac{\mu g}{2b}$
Q255 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
80 railway wagons all of same mass $5 \times 10^{3} \mathrm{~kg}$ are pulled by an engine with a force of $4 \times 10^{5} \mathrm{~N}$ . The tension in the coupling between $30^{\text{th}}$ and $31^{\text{st}}$ wagon from the engine is
A.
$25 \times 10^{4} \mathrm{~N}$
B.
$20 \times 10^{4} \mathrm{~N}$
C.
$32 \times 10^{4} \mathrm{~N}$
D.
$40 \times 10^{4} \mathrm{~N}$
Q256 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A rod of length $L$ and mass $M$ is acted on by two unequal forces $F_{1}$ and $F_{2} (< F_{1})$ as shown in the following figure. The tension in the rod at a distance $y$ from the end $A$ is given by
A.
$F_{1}\left(1 - \frac{y}{L}\right) + F_{2}\left(\frac{y}{L}\right)$
B.
$F_{2}\left(1 - \frac{y}{L}\right) + F_{1}\left(\frac{y}{L}\right)$
C.
$(F_{1} - F_{2})\frac{y}{L}$
D.
$(F_{1} - F_{2})\frac{y}{2L}$
Q257 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A disk of mass 10 g is kept floating horizontally in the air by firing bullets each of mass 5 g with the same velocity. If 10 bullets are fired per second and the bullets rebound with the same speed, then the velocity of each bullet is
A.
$196 \, cm s^{-1}$
B.
$98 \, cm s^{-1}$
C.
$49 \, cm s^{-1}$
D.
None of these
Q258 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below. The velocity of the particle after 10 s is
A.
$20\mathrm{ms}^{-1}$
B.
$10\mathrm{ms}^{-1}$
C.
$75\mathrm{ms}^{-1}$
D.
$50\mathrm{ms}^{-1}$
Q259 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is moving down a long inclined plane of slope $37^{\circ}$ . The coefficient of friction between the body and plane varies as $\mu = 0.3x$ , where x is the distance travelled down the plane. The body will have maximum speed at (Given that $\sin(37^{\circ}) = \frac{3}{5}$ and $g = 10 \, ms^{-2}$ )
A.
x = 1.16 m
B.
x = 2 m
C.
the bottom of plane
D.
x = 2.5 m
Q260 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficient of static friction and sliding friction are 0.5 and 0.4 respectively. The acceleration of the body is
A.
$6 \, ms^{-2}$
B.
$4.9 \, ms^{-2}$
C.
$3.92 \, ms^{-2}$
D.
$1 \, ms^{-2}$
Q261 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
$n$ -blocks of different masses are placed on the frictionless inclined plane in contact. They are released at the same time. The force of interaction between $(n - 1)$ th and $n$ th block is
A.
$(m_{n - 1} - m_n)g\sin \theta$
B.
zero
C.
$mng\cos \theta$
D.
None of these
Q262 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A rocket of mass 120 kg is fired in the gravity free space. It ejects gases with velocity $600 \, ms^{-1}$ at the rate of $1 \, kgs^{-1}$ . What will be the initial acceleration of the rocket?
A.
$1 \, ms^{-2}$
B.
$5 \, ms^{-2}$
C.
$10 \, ms^{-2}$
D.
$15 \, ms^{-2}$
Q263 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In order to raise a mass of 100 kg, a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $\frac{5g}{4}$ relative to the rope. The tension in the rope is $(g = 10 \, \text{ms}^{-2})$
A.
1432 N
B.
928 N
C.
1218 N
D.
642 N
Q264 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A U-shaped smooth wire has a semicircular bending between A and B as shown in the figure. A bead of mass m moving with uniform speed v through the wire enters the semicircular bend at A and leaves at B. The average force, exerted by the bead on the part AB of the wire is
A.
0
B.
$\frac{4mv^2}{\pi d}$
C.
$\frac{2mv^2}{\pi d}$
D.
None of these
Q265 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A suitcase is gently dropped on a conveyor belt moving at $3 \, ms^{-1}$ . If the coefficient of friction between the belt and the suitcase is 0.5, find the displacement of the suitcase relative to conveyor belt before the slipping between the two is stopped ( $g = 10 \, ms^{-2}$ )
A.
2.7 m
B.
1.8 m
C.
0.9 m
D.
1.2 m
Q266 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A gramophone record is revolving with an angular velocity $\omega$ . A coin is placed at a distance R from the centre of the record. The static coefficient of friction is $\mu$ . The coin will revolve with the record if
A.
$R > \frac{\mu g}{\omega^2}$
B.
$R = \frac{\mu g}{\omega^2}$ only
C.
$R < \frac{\mu g}{\omega^2}$
D.
$R \leq \frac{\mu g}{\omega^2}$
Q267 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A plank is held at an angle $\alpha$ to the horizontal (figure) on two fixed supports $A$ and $B$ . The plank can slide against the supports (without friction) because of its weight $Mg$ . Acceleration and direction in which a man of mass $m$ should move so that the plank does not move
A.
$g\sin \alpha \left[1 + \frac{m}{M}\right]$ down the incline
B.
$g\sin \alpha \left[1 + \frac{M}{m}\right]$ down the incline
C.
$g\sin \alpha \left[1 + \frac{m}{M}\right]$ up the incline
D.
$g\sin \alpha \left[1 + \frac{M}{m}\right]$ up the incline
Q268 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Given that $m_{A}=20\ kg$ , $m_{B}=10\ kg$ , $m_{C}=20\ kg$ , the coefficient of friction between B and C is $\mu_{2}=0.3$ and that between C and ground $\mu_{3}=0.1$ . The least horizontal force F to start the motion of any part of the system of three blocks resting upon one another as shown in figure is $(g=10\ ms^{-2})$
A.
$60\mathrm{N}$
B.
$90\mathrm{N}$
C.
$80\mathrm{N}$
D.
$50\mathrm{N}$
Q269 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Two blocks A and B each of mass m are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on the 2 blocks A and B respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is
A.
$F$
B.
$\frac{F}{2}$
C.
$\frac{F}{\sqrt{3}}$
D.
3F
Q270 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Two trolleys 1 and 2 are moving with acceleration $a_{1}$ and $a_{2}$ respectively in the same direction. A block of mass m on trolleys 1 is in equilibrium from the frame of observer stationary w.r.t. trolleys 2. The magnitude of friction on block due to trolley is
A.
$m\left(a_{1} - a_{2}\right)$
B.
$ma_{2}$
C.
$ma_{1}$
D.
None of these
Q271 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A conveyor belt of length l is moving with velocity v. A block of mass m is pushed against the motion of conveyor belt with velocity $v_{0}$ from end B with respect to conveyor belt. Co-efficient of friction between block and belt is $\mu$ . The value of $v_{0}$ so that the amount of heat liberated as a result of retardation of the block by conveyor belt is maximum is
A.
$\sqrt{\mu gl}$
B.
$\sqrt{2\mu gl}$
C.
$2\sqrt{\mu gl}$
D.
$\sqrt{3\mu gl}$
Q272 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Assuming that the is block always remains horizontal, hence the acceleration of $B$ is
A.
$6\mathrm{ms}^{-2}$
B.
$2\mathrm{ms}^{-2}$
C.
$4 \, ms^{-2}$
D.
None of these
Q273 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
All pulley shown in figure are light and there is no friction between pulley and string. Acceleration of pulley $P$ in figure is given by
A.
g upward
B.
g downward
C.
zero
D.
None of these
Q274 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The system shown in figure is released from rest. After blocks have moved through a distance $\frac{H}{3}$ , collar B stops and blocks A and C continue to move. The speed of C before it hits ground is
A.
$\frac{4}{3}\sqrt{gH}$
B.
$2\sqrt{\frac{gH}{3}}$
C.
$\frac{\sqrt{13gH}}{3}$
D.
$2\sqrt{2gH}$
Q275 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A block $A$ is made to move over an inclined plane of inclination $\theta$ with constant acceleration $a_0$ as shown in figure. Initially bob $B$ hanging from block $A$ is held vertical. Magnitude of acceleration of block $A$ relative to bob immediately after bob is released is
A.
$a _ {0}$
B.
$a_{0}\sin\theta$
C.
$a_{0}\cos\theta$
D.
$(a_{0}-g\sin\theta)$