**JEE Main Previous Year Papers Questions With Solutions Physics Kinematics**

**Multiple Choice with ONE correct answer**

**1.A river is flowing from west to east at a speed of 5 metre per minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction. [1983-1 mark]**

**a) due north b) 30 ° east of north**

**c) 30 ° west of north d) 60 ° east of north**

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**2.A boat which has a speed of 5 km/hr in still water crosses a river of width 1km along the shortest possible path in 15 minute. The velocity of the river in the shortest time. The velocity of river water in km/hr is [1988-1 mark]**

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**3.A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB, with speed v. Friction between the bead and the string may be neglected. Let t _{p} and t_{Q}be the respective times taken by P and Q to reach the point B. Then[1993-2 marks]**

**Ans**.(a)Horizontal displacements of both, the particle and bead, p and Q are equal Bead Q moves along AB with a constant velocity v. For particle P, motion between AC will be under acceleration while between CB will be under retardation. The horizontal component of its velocity may be greater than or equal to v. It will not be less than v.Obviously, t

_{P}< tQ.

**4.In 1.0 sec. a particle goes from point A to point B, moving in a semicircle of radius 1.0 m as shown in the figure. The magnitude of the average velocity is :**

**a) 3.14 m/sec b) 2.0 m/sec**

**c) 1.0 m/sec d) zero**

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**5.A ball is dropped vertically from a height d above the ground it hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the ground as**

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(ii)Initial velocity is downwards and therefore negative. After collision, it reverses its original direction with smaller magnitude. The velocity is upwards. Graph (a) satisfies these conditions.

**6.A body starts from rest at time t = 0, the acceleration time graph is shown in the figure. The maximum velocity attained by the body will be [2004]**

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**7.A small block slides, without friction, down an inclined plane starting from rest. Let S _{n} be the distance travelled from time t = (n – 1) to t = (n.) Then S_{n/Sn+1} is [2004-2 marks]**

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**8.The veiocity dispKiicement graph of a particle moving along a straight line is shown. The most suitable acceleration-displacement graph will be**

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**9.A ball A ball of mass 0.2 kg rests on a vertical of heights 5 m. A bullet of mass 0.01 kg, travelling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. They hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is [2011]**

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**Multiple Choice with ONE or More Than ONE correct answers**

**10.A particle is moving eastwards with a velocity of 5m/s. In 10s the velocity changes to 5m/s north wards. The average acceleration in this time is [1982-3 marks]**

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**12.The co-ordinates of a particle moving in a plane are given by x (t) = a cos (pt) and y (t) = b sin (pt) where a, b (< a) & p are positive constants of appropriate dimensions. Then [1999-3 marks]**

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**13.A sphere is rolling without slipping on a fixed horizon tal plane surface. In the figure, A is the point of V J contact, B is the centre of a the sphere and C is topmost point, Then,[2009]**

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**14.Column-I describes some situations in which a small object moves. Colymn-H describes some characteristics of these motions. Match the situations in column-I with the characteristics in column-II. [2007-6 marks]**

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**15.Column-I gives a list of possible set of parameters measured in some experiments.The variations of the parameters in the form of graphs are shown in Column-II. Match the set of parameters given in Column-I with the graphs given in Column-II.**

**Assertion & Reasoning type**

**Instructions** : The following question contains statement-I (assertion) and statement -2 (reason) of these statements, mark correct choice if

a)Statement-1 and 2 are true and statement-2 is a correct explanation for statement-1

b)Statement-l and 2 are true and statement-2 is not a correct explanation for statement-1

c)Statement-1 is true, statement-2 is flase

d)Statement-1 is false, statement-2 is true.

**16.Statement -1 : For an observer looking out through the window of a fast moving train the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.**

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**18.Is the time variation of position shown in the figure observed in nature ? [1979]**

**Ans.**If we draw a straight line parallel to x-axis, it cuts the given figure at 2 points indicating that at one time, the,particle is at two different positions which is absurd. Thus such a motion as shown in the figures is never observed in nature.

**19.Particles P and Q of mass 20 g and 40g respectively are simultaneously projected from points A and B on the ground.The initial velocities of P and Q make 45 ° and 135 ° angles respectively with the horizontal AB as shown in the figure. Each particle has an initial speed of 49m/s. The separation AB is 245m. Both particle travel in the same vertical plane and undergo a collision. After the collision, P retraces its path. Determine the position of Q when it hits the ground. How much time after the collision does the particle Q take to reach the ground ? Take g = 9.8m / s ^{2} [1982-8 marks]**

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**20.A body falling freely from a given height H hits an inclined plane in its path at a height h. As a result of this impact the direction of the velocity of the body becomes horizontal. For what value of (h/H) the body will take maximum time to reach the ground?**

**Ans.**PQR is an inclined plane. The body falls under gravity vertically from A to B till it strikes the inclined plane. At B, its velocity is horizontal. From B to C, the body follows a parabolic path. At C, it reaches the ground.

**21.Two towers AB and CD are situated a distance d apart as shown in figure. AB is 20 m high and CD is 30m high from the ground. An object of mass m is thrown from the top of AB horizontally with a velocity of lOm/s towards CD. Simultaneously another object of mass 2m is thrown from the top of CD at an angle of 60 ° ^{t0 }the horizontal towards AB with the same magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane, collide in mid-air and stick to each other [1994-4 marks]**

**i)Calculate the distance d between the towers and,**

**ii)Find the position where the objects hit the ground.**

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**23.A cart is moving along x-direction with a velocity of 4m/s. A person on the cart, throws a stone with a velocity of 6m/s, relative to himself. In the frame of reference of the cart, the stone is thrown in y-z plane making an angle of 30 ° with vertical z-axis. At the highest point of its trajectory, the stone hits an object of equal mass, hung vertically from branch of a tree, by means of a string of length L. A completely inelastic collision occurs in which the stone gets embedded in the object. Determine:[1997-5 marks]**

**i) the speed of the combined mass immediately after the collision with respect to an observer on the ground**

**ii)the length L of the string such that tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.**

**Ans.**i) The cart is moving in x-y plane

The stone, thrown from cart, travels in y-z plane while z-axis is vertical axis. The stone makes an angle of 30 ° with z-axis. Its path is parabolic. At the highest point of its trajectory, the vertical velocity of the stone will be zero. The velocity of the stone is thus confined to (x, y) plane at the highest point. Velocity of cart is along x-axis

ii)It is given that the tension in the string becomes zero at horizontal position. The combined mass therefore is at rest in this position. During the subsequent motion of the combined mass, the energy is conserved.

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**26.A particle is suspended vertically from a point O by an inextensible massless string of length L. A vertical line AB is at a distance L/8 from O as shown in figure. The object is given a horizontal velocity u. At some point, its motion ceases to be circular and eventually the object passes through the line AB. At the instant of crossing AB, its velocity is horizontal. Find u. [1999-10 marks]**

**Ans.**OP denotes string of length L. The particle starts from P with a horizontal velocity u. It travels along a circular path till Q. Then it passes the line AB. At Q, motion ceases to be circular. At C, its velocity is horizontal, where the particle crosses AB. After Q, the particle performs a projectile motion. At C, the velocity becomes horizontal. Thus C is at the highest point of projectile motion

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**29.**

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**True / False Type**

**30.Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed (Neglect air resistance).[1983-2 marks]**

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**31.’A projectile fired from the ground follows a parabolic path. The speed of the projectile, is minimum at the top of its path. [1984-2 marks]**

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**32.Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure on the rails [1985-2 marks]**

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**Fill in the blanks**

**33.A particle moves in a circle of radius R. In half the period of revolution its displacement is………. and distance covered is……… ……….. [1983-2 marks]**

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**34.Four persons K,L,M,N are initially at the four corners of a square of side d. Each person now moves with a uniform speed vin such a way that K always moves directly towards L, L directly towards M,M directly towards N, and N directly towards K. The four persons will meet at a time ………….. [1984-2 marks]**

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**36.The trajectory of a projectile in a vertical plane is y = ax-bx ^{2},where a, b are constants, and x and y are respectively the horizontal and vertical distances of the projectile from the point of projection. The maximum height attained is……….and the angle of projection from the horizontal is [1997-2 marks]**

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