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A particle of mass $200\;g$ is dropped from a height of $50\;m$ and another particle of mass $100\; g$ is simultaneously projected up from the ground along the same line with a speed of $100\; m/s$. The acceleration of the centre of mass after $1\; s$ is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 22, 2013
by
meena.p
1
answer
A cracker is thrown into air with a velocity of $10 m/s$ at an angle of $45^{\circ}$ with the vertical. When it is at a height of $0.5 \;m$ from the ground it explodes into a number of pieces which follow different parabolic paths. What is the velocity of the centre of mass when it is at a height of $1 \;m$ from the ground. $(g=10\;m/s^2)$
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 22, 2013
by
meena.p
1
answer
A particle of mass 4 m which is at rest explodes into three fragments. Two of the fragments each of mass m are found to move with speed V each in mutually perpendicular directions. The minimum energy released in the process of explosion is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 22, 2013
by
meena.p
1
answer
If $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c$ and $\overrightarrow a\times\overrightarrow b=\overrightarrow a\times\overrightarrow c$ and if $\overrightarrow a\neq 0$, then
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q59
asked
Nov 21, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors then $(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times (\overrightarrow c+\overrightarrow a)=?$
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
vector-product
q58
asked
Nov 21, 2013
by
rvidyagovindarajan_1
1
answer
If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors, then $[\overrightarrow a+\overrightarrow b+\overrightarrow c\:\overrightarrow a-\overrightarrow c\:\overrightarrow a-\overrightarrow b]=?$
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q57
asked
Nov 21, 2013
by
rvidyagovindarajan_1
1
answer
Two particles A and B initially at must move towards each other under a mutual force of attraction. The speed of the center of mass at the instant speed of A is V and the speed of B is 2V is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Internal forces in a system can change
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Two particles having mass ratio $n:1$ are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of centre of mass of the system is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 21, 2013
by
meena.p
1
answer
A uniform sphere is placed on a smooth horizontal surface and a horizontal force f is applied on it at a distance h above the center. The acceleration of the center of mass of the sphere
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Two particles of equal mass have velocities $\overrightarrow{V_1}=4 \hat {i}$ and $V_2= 4 \hat {j} m/s$. First particle has an accleration $\overrightarrow{a_1}=(5 \hat i+5 \hat{j})m/s^2$ While the acceleration of the other particle is zero. The center of mass of the two particles moves in a path of
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 21, 2013
by
meena.p
1
answer
For positive numbers $x,y$ and $z$ the numerical value of the determinant $\begin{vmatrix}1 &\log_xy&\log_xz\\\log_yx&1&\log_yz\\\log_zx&\log_zy&1\end{vmatrix}$ is
jeemain
math
class12
ch4
determinants
q3
properties-of-determinants
medium
asked
Nov 21, 2013
by
sreemathi.v
1
answer
A trolley of mass 360 kg lying on a horizontal friction less surface. A man of mass 40 kg runs with uniform speed on the trolley a distance of 2 m in $0.5 \;s$. What is the velocity of the trolley relative to the earth?
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
A man of mass 40 kg is standing on a uniform Planck of mass 60 kg lying on a horizontal friction less ice. The man walks from one end to the other end of the Planck. The distance walked by the man relative to ice is (length of Planck=5 m)
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Let $a,b,c$ be the real numbers. Then the following system of equations in $x,y$ and $z$: $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$, $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$, $\large\frac{-x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ has
jeemain
math
class12
ch4
determinants
q2
system-of-linear-equations
medium
asked
Nov 21, 2013
by
sreemathi.v
1
answer
A shell projected from a level ground has a range R, it does not explode. At the highest point the shell explodes into two fragments having masses in the radio 1:3 with each fragment moving horizontally immediately after the explosion. If the lighter fragment falls at a distance R from the point of projection, the distance at which the other fragment falls from the point of projection is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Let $p\lambda^4+q\lambda^3+r\lambda^2+s\lambda+t$ = $\begin{vmatrix}\lambda^3+3\lambda&\lambda-1&\lambda+3\\\lambda+1&-2\lambda&\lambda-4\\\lambda-3&\lambda+4&3\lambda\end{vmatrix}$ be an identity in $\lambda$ where $p,q,r,s$ and $t$ are constant. Then the value of $t$ is
jeemain
math
class12
ch4
determinants
q1
system-of-linear-equations
medium
asked
Nov 21, 2013
by
sreemathi.v
1
answer
A shell is projected from a level ground with a velocity of $20\;m/s$ at $45^{\circ}$ to the horizontal. When the shell is at highest point, it breaks into two equal fragments. One of the fragment whose initial velocity after the explosion is zero, falls vertically downward. At what distance from the point of projection does the other fragment fall? $(g=10\;ms^{-2})$
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
A shell in flight explodes into n equal fragments. K of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Inverse of $\begin{bmatrix}1&2&3\\2&3&4\\3&4&6\end{bmatrix}$ is
jeemain
math
class12
ch4
matrices-and-determinants
q50
adjoint-and-inverse
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
If $B$ is a non-singular matrix and A is a square matrix then $det(B^{-1}AB)$ is equal to
jeemain
math
class12
ch4
determinants
q49
adjoint-and-inverse
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
A balloon of mass M is stationary in air. It has a ladder on which a man of mass m is standing. If the man starts climbing up the ladder with a velocity v relative to the ladder, the velocity of the balloon is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Two blocks of masses 4 kg and 3 kg are placed on a friction less surface connected by a string. An external force gives a velocity 7 m/s to the heavier mass in the direction of the lighter , velocity of their centre of mass is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
If $A$ is a square matrix such that $A^2=I$ then $A^{-1}$ is equal to
jeemain
math
class12
ch3
matrices
q48
transpose-of-a-matrix
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Two particles of mass 2m and 3m are at a distance 'd' apart. Under their mutual gravitational force, they start moving towards each other. The acceleration of their center of mass when they are $d/2$ apart is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Two bodies of masses 10 kg and 2 kg are moving with velocities $2m/s$ and $10m/s$, towards each other . The velocity of their centre of mass is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
A boy of mass 36 kg moves from one end to other end of a boat of mass 72 kg on still water. If the length of the boat is 2.7 m, the displacement of the boat is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
If $a_1,a_2,a_3.......a_n$ are in G.P then the value of the determinant $\begin{vmatrix}\log a_n&\log a_{n+1}&\log a_{n+2}\\\log a_{n+3}&\log a_{n+4}&\log a_{n+5}\\\log a_{n+6}&\log a_{n+7}&\log a_{n+8}\end{vmatrix}$ is
jeemain
math
class12
ch4
determinants
q47
evaluate-determinants
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Two particles A and B of masses 2 kg and 3 kg are separated by 10 m. If they move towards each other under a mutual force of attraction, the distance of the point where they meet from the initial position of A is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Let $A=\begin{vmatrix}5 &5\alpha&\alpha\\0&\alpha&5\alpha\\0&0&5\end{vmatrix}$ if $\mid A^2\mid=25$ then $\alpha$ equals
jeemain
math
class12
ch3
matrices
q46
invertible-matrices
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Three particles of masses 8 kg, 4 kg and 4 kg situated at $(4,1),(-2,2)$ and $(1,-3)m$ are acted upon by external forces $6 \hat {j},-6 \hat {i}$ and $14 \hat {i}\;N$ respectively . The acceleration of the center of Mass of the system is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
If $D=\begin{vmatrix}1&1&1\\1&1+x&1\\1&1&1+y\end{vmatrix}$ for $x\neq 0,y\neq 0$ then $D$ is
jeemain
math
class12
ch4
determinants
q45
evaluate-determinants
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Two particles of masses 1 kg and 3 kg have velocities $(2 \hat i-3 \hat j+4 \hat k)ms^{-1}$ and $(4 \hat {i}+2 \hat j+\hat k)ms^{-1}$ at a given instant of time. The velocity of the center of mass is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
easy
asked
Nov 21, 2013
by
meena.p
1
answer
Let $A=\begin{bmatrix}1&2\\3&4\end{bmatrix}$ and $B=\begin{bmatrix}a&0\\0&b\end{bmatrix}\;a,b\in N$.Then
jeemain
math
class12
ch3
matrices
q44
equality-of-matrices
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
A uniform circular sheet has a radius r. A square sheet whose diagonal length is equal to the radius of the plate is removed. The maximum distance of the centre of mass of the square sheet from the center of original sheet is :
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 21, 2013
by
meena.p
1
answer
If $A$ and $B$ are square matrices of size $n\times n$ such that $A^2-B^2=(A-B)(A+B)$ then which of the following will be always true?
jeemain
math
class12
ch3
matrices
q43
invertible-matrices
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
If $A^2-A+I=0$ then the inverse of A is
jeemain
math
class12
ch4
determinants
q42
adjoint-and-inverse
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 &-1&1\\2&1&-3\\1&1&1\end{bmatrix}$ and $10B=\begin{bmatrix}4 &2&2\\-5&0&\alpha\\1&-2&3\end{bmatrix}$ if $B$ is the inverse of matrix A then $\alpha$ is
jeemain
math
class12
ch4
determinants
q41
adjoint-and-inverse
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}0 &0&-1\\0&-1&0\\-1&0&0\end{bmatrix}$.The only correct statement about the matrix A is
jeemain
math
class12
ch4
determinants
q40
adjoint-and-inverse
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
A uniform metal rod is bent units L-shaped with the bent arms at 90 to each other. The distance of the center of mass of the remaining portion from the center of the original sheet is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 21, 2013
by
meena.p
1
answer
If $A=\begin{bmatrix}a&b\\b&a\end{bmatrix}$ and $A^2=\begin{bmatrix}\alpha&\beta\\\beta&\alpha\end{bmatrix}$ then
jeemain
math
class12
ch3
matrices
q39
operations-on-matrices
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
If $1,\omega,\omega^2$ are the cube roots of unity ,then $\Delta=\begin{vmatrix}1&\omega^n&\omega^{2n}\\\omega^{2n}&1&\omega^n\\\omega^{2n}&1&\omega^n\end{vmatrix}$ is equal to
jeemain
math
class12
ch4
determinants
q38
evaluate-determinants
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
A uniform square sheet has a side of length $2R$. A circular sheet of maximum possible area is removed from one of the quadrants of the square sheet. The distance of the center of mass of the remaining portion from the center of the original sheet is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 21, 2013
by
meena.p
1
answer
If the system of linear equations $x+2ay+az=0,x+3by+bz=0,x+4cy+cz=0$ has a non-zero solution the a,b,c
jeemain
math
class12
ch4
determinants
q37
system-of-linear equations
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
If $a>0$ and determinant of $ax^2+2bx+c$ is -ve then $\begin{vmatrix}a&b&ax+b\\b&c&bx+c\\ax+b&bx+c&0\end{vmatrix}$ is equal to
jeemain
math
class12
ch4
determinants
q36
evaluate-determinants
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Let $\omega$ be a complex cube root of unity with $\omega\neq 1$ and $p=[P_{ij}]$ be a $n\times n$ matrix with $P_{ij}=\omega^{i+j}$.Then $P^2\neq 0$ when $n$=
jeemain
math
class12
ch3
matrices
q35
operations-on-matrices
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
If the adjoint of a $3\times 3$ matrix P is $\begin{bmatrix}1 &4&4\\2&1&7\\1&1&3\end{bmatrix}$ then the possible value(s) of the determinant of P is
jeemain
math
class12
ch4
determinants
q34
adjoint-and-inverse
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
Let $M$ and $N$ be two $3\times 3$ non singular skew-symmetric matrices such that $MN=NM$.If PT denotes the transpose of P,then $M^2N^2(M^TN)^{-1}(MN^{-1})^T$ is equal to
jeemain
math
class12
ch3
matrices
q33
symmetric-and-skew-symmetric-matrices
easy
asked
Nov 21, 2013
by
sreemathi.v
1
answer
From a sphere of radius 1m, a sphere of radius 0.5 m is removed from the edge. The shift in the CM is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 21, 2013
by
meena.p
1
answer
Half of the uniform rectangular plate of length 'L' is made of material of density $d_1$and the other half of density $d_2$. The horizontal distance of center of mass from AB is
jeemain
physics
class11
unit5a
center-of-mass-and-collisions
medium
asked
Nov 21, 2013
by
meena.p
1
answer
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