Conservation of Mechanical Energy

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JEE Main 2021, 20 July Shift-I

LEVELJEE Main

In a spring gun having spring constant $100 N/m$ a small ball $B$ of mass $100 g$ is put in its barrel (as shown in figure) by compressing the spring through $0.05 m$ . There should be a box placed at a distance $d$ on the ground, so that the ball falls in it. If the ball leaves the gun horizontally at a height of $2 m$ above the ground. The value of $d$ is ……… m. (Take, $g = 10 m/s^{2}$ )

JEE Main 2020, 3 Sep Shift-II

LEVELJEE Main

A block of mass 1.9 kg is at rest at the edge of a table of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision, then the kinetic energy just before the combined system strikes the floor, is (Take, $g = 10 m/s^{2}$ and assume there is no rotational motion and loss of energy after the collision is negligible)

JEE Main 2021, 26 Aug Shift-I

LEVELJEE Main

A uniform chain of length 3 m and mass 3 kg overhangs a smooth table with 2 m laying on the table. If $k$ is the kinetic energy of the chain in joule as it completely slips off the table, then the value of $k$ is ......... . (Take, $g = 10 m/s^{2}$ )

LEVELJEE Main

The block of mass $M$ moving on the frictionless horizontal surface collides with the spring of spring constant $k$ and compresses it by length $L$ . The maximum momentum of the block after collision is

(A)

M k L

(B)

\frac{k L ^{2}}{2 M}

(C)

zero

(D)

\frac{M L ^{2}}{k}

JEE Main 2021, 27 July Shift-II

LEVELJEE Main

Given below is the plot of a potential energy function $U (x)$ for a system, in which a particle is in one-dimensional motion, while a conservative force $F (x)$ acts on it. Suppose that $E_{mech} = 8 J$ , the incorrect statement for this system is [where, $KE = kinetic energy$ ]

(A)

x > x_{4}

, KE is constant throughout the region.

(B)

x < x_{1}

, KE is smallest and the particle is moving at the slowest speed.

(C)

x = x_{2}

, KE is greatest and the particle is moving at the fastest speed.

(D)

x = x_{3}

KE = 4 J

JEE Main 2020

LEVELJEE Main

A particle ( $m = 1 kg$ ) slides down a frictionless track ( $A O C$ ) starting from rest at a point $A$ (height 2 m). After reaching $C$ , the particle continues to move freely in air as a projectile. When it reaching its highest point $P$ (height 1 m), the kinetic energy of the particle (in J) is : (Figure drawn is schematic and not to scale; take $g = 10 ms^{- 2}$ ) ......... .

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

As shown in the figure, a particle of mass $10 kg$ is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is $x m/s$ . (Take, $g = 10 m/s^{2}$ ) The value of $x$ to the nearest integer is ....... .

LEVELJEE Main

A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is

1030

m/s

LEVELJEE Advanced

The potential energy of a $1 kg$ particle free to move along the x-axis is given by $V (x) = (\frac{x ^{4}}{4} - \frac{x ^{2}}{2}) J$ The total mechanical energy of the particle is $2 J$ . Then, the maximum speed (in $ms^{- 1}$ ) is

(A)

\frac{3}{2}

(B)

2

(C)

\frac{1}{2}

(D)

2

JEE Main 2019, 11 Jan Shift-I

LEVELJEE Advanced

A body of mass $1 kg$ falls freely from a height of $100 m$ on a platform of mass $3 kg$ which is mounted on a spring having spring constant $k = 1.25 \times 1 0^{6} N/m$ . The body sticks to the platform and the spring's maximum compression is found to be $x$ . Given that $g = 10 ms^{- 2}$ , the value of $x$ will be close to

(A)

8 cm

(B)

4 cm

(C)

40 cm

(D)

80 cm

JEE Main 2021, 18 March Shift-II

LEVELJEE Main

A ball of mass $4 kg$ , moving with a velocity of $10 ms^{- 1}$ , collides with a spring of length $8 m$ and force constant $100 Nm^{- 1}$ . The length of the compressed spring is $x m$ . The value of $x$ to the nearest integer, is ............ .

LEVELJEE Main

From a building, two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then

(A)

v_{B} > v_{A}

(B)

v_{A} = v_{B}

(C)

v_{A} > v_{B}

(D)

their velocities depend on their masses

JEE Advanced 2007

LEVELJEE Main

Assertion A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$ . It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $3 0^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$ . The decrease in the mechanical energy in the second situation is smaller than that in the first situation. Reason The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

(A)

(a) If Assertion is true, Reason is true; Reason is the correct explanation for Assertion

(B)

(b) If Assertion is true, Reason is true; Reason is not a correct explanation for Assertion

(C)

(D)

(d) If Assertion is false; Reason is true

JEE Advanced 2008

LEVELJEE Advanced

A block ( $B$ ) is attached to two unstretched springs $S_{1}$ and $S_{2}$ with spring constants $k$ and $4 k$ , respectively. The other ends are attached to two supports $M_{1}$ and $M_{2}$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall 1 by a small distance $x$ and released. The block returns and moves a maximum distance $y$ towards wall 2. Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block $B$ . The ratio $\frac{y}{x}$ is

(A)

(B)

(C)

\frac{1}{2}

(D)

\frac{1}{4}

JEE Advanced (2008)

LEVELJEE Advanced

Comprehension Passage

A small block of mass

M

moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from

6 0^{\circ}

3 0^{\circ}

at point

B

. The block is initially at rest at

A

. Assume that collisions between the block and the incline are totally inelastic(

g = 10 m/s^{2}

JEE Advanced (2002)

LEVELJEE Main

An ideal spring with spring constant $k$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

(A)

\frac{4 M g}{k}

(B)

\frac{2 M g}{k}

(C)

\frac{M g}{k}

(D)

\frac{M g}{2 k}

JEE Advanced 2020

LEVELJEE Advanced

A student skates up a ramp that makes an angle $3 0^{\circ}$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_{0}$ and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

* Multiple Correct Options

(A)

v_{0}^{2} - 2 g h = \frac{1}{2} g R

(B)

v_{0}^{2} - 2 g h = \frac{3}{2} g R

(C)

the centripetal force required at points x and z is zero

(D)

the centripetal force required is maximum at points x and z