Question 1 :
When a ball is thrown up vertically with velocity {tex} v _ { 0 } , {/tex} it reaches a maximum height of {tex} h {/tex} . If one wishes to triple the maximum height then the ball should be thrown with velocity
Question 2 :
A passenger, observer A, in a car traveling at a constant horizontal velocity of magnitude 60 mi/h pour a cup of coffee for the tired driver. Observer B stands on the side of the road and watches the pouring process through the window of the car as it passes. Which observer(s) sees a parabolic path for the coffee as it moves through the air ?
Question 3 :
A wheel covers a distance of 9.5 km in 2000 revolutions. The diameter of the wheel is
Question 4 :
During an accelerated motion of a particle (initial velocity of particle is zero)
Question 5 :
A circular track or radius 100 m is designed for an average speed 54 km/h. Find the angle of banking.
Question 6 :
If a body is projected with an angle θ to the horizontal, then -
Question 7 : Four girls skating on circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in figure. For which girl displacement is equal to the actual length of path skate?<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e2ea4389b1556ddefd7b' height='131' width='110' >
Question 8 :
A bullet is fired with a gun from a tower horizontally with a velocity 400 m/s. At the same time a stone is dropped from the same tower
Question 9 : A stone is to hit a point which is at a distance <em>d</em> away and at a height <em>h</em> above the point from where the stone is projected. The value of initial speed <em>u</em> if the stone is projected at an angle θ will be <br/> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd771da6d070c2abf84e"/>
Question 10 :
A particle does uniform circular motion in a horizontal plane. The radius of the circle is {tex} 20 \mathrm { cm } {/tex}. The centripetal force acting on the particle is {tex} 10 \mathrm { N } {/tex}. It's kinetic energy is
Question 11 :
A road is 5 m wide. Its radius of curvature is {tex}20 \sqrt { 6 } \mathrm { m } {/tex} . The outer edge is above the inner edge by a distance of {tex} \mathrm { f } {/tex} {tex} 1 \mathrm { m } {/tex} . This road is most suited for a speed {tex} \left( g = 10 \mathrm { ms } ^ { - 2 } \right) {/tex}
Question 12 :
A particle moving in a straight line has velocity and displacement equation as {tex} v = 4 \sqrt { 1 + s } , {/tex} where {tex} v {/tex} is in {tex} \mathrm { m } / \mathrm { s } {/tex} and {tex} s {/tex} is in {tex} \mathrm { m } {/tex} . The initial velocity of the particle is
Question 13 : Trajectories of two projectiles are shown in the figure. Let T<sub>1</sub> and T<sub>2</sub> be the time of flights and u<sub>1</sub> and u<sub>2</sub>be their speeds of projection. Then - <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e824491ec95800698151' height='76' width='111' >
Question 14 :
A body is revolving with a uniform speed {tex} v {/tex} in a circle of radius {tex} r . {/tex} The tangential acceleration is
Question 15 : The velocity-time curve of a body is shown in figure. The average speed of the body in first seven second is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd494bec8070e4e14f53"/>
Question 16 :
A man can row a boat with speed 4 km/hr in still water. If the velocity of water in river is 3 km/hr. The time taken to reach just opposite end is (river width = 500 m)
Question 17 :
The two ends of a train moving with constant acceleration pass a certain point with velocities <em>u</em> and <em>v</em>. The velocity with which the middle point of the train passes the same point is
Question 18 : The velocity of a particle that moves in the positive <em>x</em>-direction varies with its position (<em>x</em>) as shown in figure. Its acceleration at <em>x</em> = 6 m is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd7d4bec8070e4e14f8a"/>
Question 19 :
A body is thrown with the velocity {tex} v _ { 0 } {/tex} at an angle {tex} \alpha {/tex} with the horizontal. If the body remains in air for the time {tex} t = 4 s {/tex} , the maximum height reached by the body will be
Question 20 :
Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first ?
Question 21 :
The retardation of a particle moving in a straight line is proportional to its displacement (proportionality con- stant being unity). Initial velocity of the particle is {tex} v _ { 0 } {/tex} . Find the total displacement of the particle till it comes to rest.
Question 22 :
A coin placed on a rotating turntable just slips if it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of -
Question 23 :
If the initial velocity of a projectile be doubled. Keeping the angle of projection same, the maximum height reached by it will
Question 24 :
Consider the following controls in an automobile: gas pedal, brake, steering wheel. The controls in this list that cause an acceleration of the car are -
Question 25 :
A particle has an initial velocity 11{tex} \mathrm { m } / \mathrm { s } {/tex} due east and a constant acceleration of 2{tex} \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} due west. The distance covered by the particle in sixth second is
Question 26 :
A body is thrown with the velocity {tex} v _ { 0 } {/tex} at an angle {tex} \alpha {/tex} with the horizontal. If the body remains in air for 6{tex} \mathrm { s } {/tex} the maximum height reached by the body will be
Question 27 :
A body is projected at an angle of 30<sup>0</sup> with the horizontal with momentum p. At its highest point, the momentum is -
Question 28 :
A projectile has the same range <em>R</em> for two angles of projection. If <em>T</em><sub>1</sub> and <em>T</em><sub>2</sub> be the times of flight in the two cases, then <em>R</em> is
Question 29 :
Acceleration of a particle moving along a straight line is a function of velocity as {tex}a = 2\sqrt{v}\text{.}{/tex} At <em>t</em> = 2<em>s</em>, its velocity <em>v</em> = 16ms<sup> − 1</sup>. Its velocity at <em>t</em> = 3<em>s</em> will be
Question 30 :
The x and y coordinates of a particle at any time t are given by x = 2t + 4t<sup>2</sup> and y = 5t, where x and y are in meter and t in second. The acceleration of the particle at t =5 s is -
Question 31 :
A particle is moving in positive <em>x</em>– direction with initial velocity of 10 m/s and uniform retardation such that it reaches the initial position after 10s. The distance traversed by the particle in 6 seconds is
Question 32 :
For a body moving in a circular path, a condition for no skidding if {tex} \mu {/tex} is the coefficient of friction, is
Question 33 :
Two bodies are projected with the same velocity. If one is projected at an angle of 30<sup>o</sup> and the other at an angle of 60<sup>o</sup> to the horizontal, the ratio of the maximum heights reached is
Question 34 :
The magnitude of displacement is equal to the distance covered in a given internal of time if the particle
Question 35 :
A stone is thrown form a cliff of height h in a given direction then the speed with which it hits ground -
Question 37 :
A swimmer wishes to cross a 800 m wide river flowing at 6 km/hr. His speed with respect to water is 4 km/hr. He crosses the river in shortest possible time. He is drifted downstream on reaching the other bank by a distance of
Question 38 :
A string of length 1m is fixed at one end and carries a mass of 100 g at the other end. The string makes 2/π revolutions per second around the vertical axis through the fixed end. If angle of inclination of the string with the vertical is cos<sup>-1</sup>5/8, the linear velocity of the mass is nearly
Question 39 :
A pebble is thrown vertically upwards from a bridge with an initial velocity of 10 ms<sup>–1</sup>. It strikes water after 5s. The height of the bridge is (<em>g</em> = 10 m/s<sup>2</sup>)
Question 40 :
Two bodies are projected vertically upwards from one point with the same initial velocities <em>v</em><sub>0</sub> m/s. The second body is thrown τ s after the first. The two bodies meet after time
Question 41 : A particle moves along the sides <em>AB</em>, <em>BC</em>, <em>CD</em> of a square of side 25 m with a velocity of 15m/s. Its average velocity is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd591da6d070c2abf82a"/>
Question 42 :
The initial velocity of a particle moving along a straight line is 12 ms<sup>–1</sup> and its retardation is<br/> 3 ms<sup>–2</sup>. The distance moved by the particle in the fourth second of its motion is
Question 43 :
A cylindrical vessel partially filled with water is rotated about its vertical central axis. It's surface will
Question 44 :
The acceleration of a particle, starting from rest, varies with time according to the relation <em>a</em> = <em>k</em> <em>t</em> + <em>c</em>. The velocity <em>v</em> of the particle after a time <em>t</em> will be
Question 45 :
A bus is moving with a velocity {tex}10{tex} \mathrm { ms } ^ { - 1 } {/tex} on a straight road. A motorist wishes to overtake the bus in 100{tex} \mathrm { s } {/tex} . If the bus is at a distance of {tex}1{tex} \mathrm { km } {/tex} from the motorist, with what velocity should the motorist chase the bus?
Question 46 :
A football is kicked into the air vertically upwards with velocity u. The velocity of the ball at the highest point is
Question 47 : A jeep moves at uniform speed of 60 kmh<sup>-1</sup> on a straight road blocked by a wall. The jeep has to take a sharp perpendicular turn along the wall. A rocket flying at uniform speed of 100 kmh<sup>-1</sup> starts from the wall towards the jeep when the jeep is 30 km away. The rocket reaches the windscreen and returns to wall. Total distance covered by the rocket is<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e5b4b5f89758f2d4ef53' height='116' width='201' >
Question 48 :
A body is projected such that its KE at the top is 3/4th of its initial KE. What is the angle of projectile with the horizontal?
Question 49 :
A point moves on the xy plane according to the law x = a sin ωt and y = a(1 - cosωt) where a and ω are positive constants. Find the distance covered in time t<sub>0</sub>.
Question 50 :
A stuntman plans to run across a roof top and then horizontally off it to land on the roof of the next building. The roof of the next building is 4.9 m below the first one and 6.2 m away from it. The minimum roof top speed for successful jump is -
