Difficult
$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
According to the observer $A$:
$A$: standing on the horizontal surface
$B$: standing on the block
According to the observer $A$:
- Athe kinetic energy of the block is converted into the potential energy of the spring
- Bthe mechanical energy of the spring-mass system is conserved
- Cthe block loses its kinetic energy because of the negative work done by the conservative force of spring
- Dall the above
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$A$ section of a fixed smooth circular track of radius $R$ in a vertical plane is shown in the figure. $A$ block is released from position $A$ and leaves the track at $B$. The radius of curvature of its trajectory when it just leaves the track at $B$ is:
Difficult
View Solution$A$ target is made of two plates,one of wood and the other of iron. The thickness of the wooden plate is $4\,cm$ and that of the iron plate is $2\,cm$. $A$ bullet fired goes through the wood first and then penetrates $1\,cm$ into the iron. $A$ similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\,cm$ into the wood. If $a_1$ and $a_2$ are the retardations offered to the bullet by the wood and iron plates respectively,then:
Three objects $A$,$B$,and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m$,$2m$,and $m$,respectively. The object $A$ moves towards $B$ with a speed of $9 \ m/s$ and makes an elastic collision with it. Thereafter,$B$ makes a completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in $m/s$) of the object $C$.
DifficultIIT 2009
View SolutionIn two separate collisions,the coefficients of restitution $e_1$ and $e_2$ are in the ratio $3: 1$. In the first collision,the relative velocity of approach is twice the relative velocity of separation. Then,the ratio between the relative velocity of approach and the relative velocity of separation in the second collision is:
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